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On restricted edge-colorings of bicliques

Dhruv Mubayi, Douglas B. West
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We investigate the minimum and maximum number of colors in edge-colorings of Kn;n such that every copy of Kp;p receives at least q and at most q colors.  ...  Along the way we improve the bounds on some bipartite Turà an numbers.  ...  The restricted generalized Ramsey problem is itself a special case of constrained hypergraph coloring.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(02)00510-1">doi:10.1016/s0012-365x(02)00510-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g35uqwoptjhurk6t3baarxm42m">fatcat:g35uqwoptjhurk6t3baarxm42m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190305140041/https://core.ac.uk/download/pdf/81215191.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/f0/2af01543b080443bcbb570b6ce867881e3ea1863.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(02)00510-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Confluent Layered Drawings

David Eppstein, Michael T. Goodrich, Jeremy Yu Meng
<span title="">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
The biclique cover problem is reduced to a special edge coloring problem and solved by heuristic coloring algorithms. Our method can be extended to obtain multi-depth confluent layered drawings.  ...  We combine the idea of confluent drawings with Sugiyama style drawings, in order to reduce the edge crossings in the resultant drawings.  ...  By computing a simply restricted edge coloring we can get a biclique cover of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-006-0159-8">doi:10.1007/s00453-006-0159-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2bdu4vytcrh6thzc6adzp2gz4u">fatcat:2bdu4vytcrh6thzc6adzp2gz4u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20061211130033/http://www.ics.uci.edu:80/~goodrich/pubs/conflayer-alg.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ed/99/ed99067cf722d785f2e2ba917cbf54488c5978d9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-006-0159-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Confluent Layered Drawings [chapter]

David Eppstein, Michael T. Goodrich, Jeremy Yu Meng
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The biclique cover problem is reduced to a special edge coloring problem and solved by heuristic coloring algorithms. Our method can be extended to obtain multi-depth confluent layered drawings.  ...  We combine the idea of confluent drawings with Sugiyama style drawings, in order to reduce the edge crossings in the resultant drawings.  ...  By computing a simply restricted edge coloring we can get a biclique cover of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31843-9_20">doi:10.1007/978-3-540-31843-9_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b3sh32g5w5eotnjfo747jey5fe">fatcat:b3sh32g5w5eotnjfo747jey5fe</a> </span>
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On star and biclique edge-colorings

Simone Dantas, Marina Groshaus, André Guedes, Raphael C. S. Machado, Bernard Ries, Diana Sasaki
<span title="2016-06-02">2016</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2vyq3vorabczbc57sgxyrmy42y" style="color: black;">International Transactions in Operational Research</a> </i> &nbsp;
A biclique (resp. star) edge-coloring is a coloring of the edges of a graph with no monochromatic bicliques (resp. stars).  ...  A biclique of G is a maximal set of vertices that induces a complete bipartite subgraph K p,q of G with at least one edge, and a star of a graph G is a maximal set of vertices that induces a complete bipartite  ...  The NP-hardness of biclique (resp. star) edge-coloring using two colors motivates the study of these two problems in restricted graph classes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/itor.12307">doi:10.1111/itor.12307</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/txsnz7oszza4nhi5nbpiqoro4m">fatcat:txsnz7oszza4nhi5nbpiqoro4m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427072330/http://doc.rero.ch/record/324393/files/biclique_rero.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6d/dd/6ddddd16292f4f06fc394100dce7c2fb7347aae0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/itor.12307"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Covering graphs with few complete bipartite subgraphs

Herbert Fleischner, Egbert Mujuni, Daniël Paulusma, Stefan Szeider
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional  ...  We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs).  ...  The second author's research was supported by International Science Programme (ISP) of Sweden, under the project ''The Eastern African Universities Mathematics Programme (EAUMP).''  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2008.12.059">doi:10.1016/j.tcs.2008.12.059</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ppshskddmbakfj5r2e2pheenb4">fatcat:ppshskddmbakfj5r2e2pheenb4</a> </span>
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Covering Graphs with Few Complete Bipartite Subgraphs [chapter]

Herbert Fleischner, Egbert Mujuni, Daniel Paulusma, Stefan Szeider
<span title="">2007</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
There, the minimum number of bicliques necessary to cover all the edges of a  ...  G is contained in at least one of the subgraphs in S. The set S is a vertex-cover of G if every vertex of G is contained in at least one of the subgraphs in S.  ...  In view of the NP-hardness it makes sense to study the more restricted problem b-Biclique Vertex-Cover where the bicliques in the cover are bicliques where at least one of the bipartite sets contains at  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-77050-3_28">doi:10.1007/978-3-540-77050-3_28</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3veh3svmendplpbl6ogtow6hhy">fatcat:3veh3svmendplpbl6ogtow6hhy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090625182729/http://www.dur.ac.uk/stefan.szeider/papers/biclique.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3b/c7/3bc703114f10ca8ecd70c5f1bc8dc4d47f4bb822.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-77050-3_28"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Clique-Colouring and Biclique-Colouring Unichord-Free Graphs [chapter]

Hélio B. Macêdo Filho, Raphael C. S. Machado, Celina M. H. Figueiredo
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In the present work, we investigate clique-colouring and biclique-colouring problems restricted to unichord-free graphs.  ...  The class of unichord-free graphs was recently investigated in the context of vertex-colouring [J. Graph Theory 63 (2010) 31-67], edge-colouring [Theoret. Comput.  ...  the biclique-colouring problem restricted to unichord-free graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-29344-3_45">doi:10.1007/978-3-642-29344-3_45</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tl2uy7pl5nby5aq6zadwqyds7i">fatcat:tl2uy7pl5nby5aq6zadwqyds7i</a> </span>
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Biclique graphs and biclique matrices

Marina Groshaus, Jayme L. Szwarcfiter
<span title="">2010</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ukzsjb6a6zhyxnjl6nb2mmjc6m" style="color: black;">Journal of Graph Theory</a> </i> &nbsp;
Given a graph G, the biclique matrix of G is a {0, 1, −1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, −1 entries in a same row corresponds exactly  ...  We describe a characterization of biclique matrices, in similar terms as those employed in Gilmore's characterization of clique matrices. On the other hand, the  ...  On the other hand, the coloring restricted to the partial hypergraph formed by the hyperedges E 1 and E 3 is compatible.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jgt.20442">doi:10.1002/jgt.20442</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5zyu2x5z5bfdba7g6wfqsmpcie">fatcat:5zyu2x5z5bfdba7g6wfqsmpcie</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706041431/http://publicaciones.dc.uba.ar/Publications/2010/GS10/Biclique%20graphs%20-%20JGT.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/25/31/2531d1ba6a347fdb38d1a0678e0b52fecda67d45.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jgt.20442"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Biclique Coverings and the Chromatic Number [article]

Dhruv Mubayi, Sundar Vishwanathan
<span title="2009-03-17">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Consider a graph G with chromatic number k and a collection of complete bipartite graphs, or bicliques, that cover the edges of G.  ...  We prove the following two results: ∙ If the bicliques partition the edges of G, then their number is at least 2^√(_2 k).  ...  Acknowledgments The research of Dhruv Mubayi was supported in part by NSF grant DMS 0653946.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0903.3048v1">arXiv:0903.3048v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fkitwrapdnghbii2duylzvcty4">fatcat:fkitwrapdnghbii2duylzvcty4</a> </span>
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Mining Stable Roles in RBAC [chapter]

Alessandro Colantonio, Roberto Di Pietro, Alberto Ocello, Nino Vincenzo Verde
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kss7mrolvja63k4rmix3iynkzi" style="color: black;">IFIP Advances in Information and Communication Technology</a> </i> &nbsp;
methodology: first, we associate a weight to roles; second, we identify and remove the user-permission assignments that cannot belong to a role that have a weight exceeding a given threshold; third, we restrict  ...  Finally, we discuss practical applications of our approach to the role mining problem.  ...  Thus, in a biclique cover, each edge of G is covered at least by one biclique. A minimum biclique cover (MBC) is the smallest collection of bicliques that covers the edges of a given bipartite graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-01244-0_23">doi:10.1007/978-3-642-01244-0_23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cf63nfxr3jaktgb2euouxap5qm">fatcat:cf63nfxr3jaktgb2euouxap5qm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151229000014/http://dl.ifip.org/db/conf/sec/sec2009/ColantonioPOV09.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/38/9f38b7a9a90e5257747a386a3c669ff0d69fb92c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-01244-0_23"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The Star and Biclique Coloring and Choosability Problems

Marina Groshaus, Francisco J. Soulignac, Pablo Terlisky
<span title="">2014</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques).  ...  Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, threshold graphs, and net-free  ...  The remaining sections of the article study the star and biclique coloring problems on graphs with restricted inputs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00326">doi:10.7155/jgaa.00326</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/45gbdch7xjg3xau5hqy4jgcsaq">fatcat:45gbdch7xjg3xau5hqy4jgcsaq</a> </span>
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Algorithms for recognizing bipartite-Helly and bipartite-conformal hypergraphs,

Marina Groshaus, Jayme Luis Szwarcfiter
<span title="">2011</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/inei2pvlvnaw7lwfzvf7meb67e" style="color: black;">Reserche operationelle</a> </i> &nbsp;
We consider the concepts of bipartite-conformal and (colored) bipartite-Helly hypergraphs.  ...  They are useful for characterizing biclique matrices and biclique graphs, that is, the incident biclique-vertex incidence matrix and the intersection graphs of the maximal bicliques of a graph, respectively  ...  On the other hand, we use bipartite-Helly hypergraphs to prove a result on biclique graphs, that is, the intersection graphs of the bicliques of a graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ro/2011112">doi:10.1051/ro/2011112</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n2zloffrn5dc7f4varbfkry64m">fatcat:n2zloffrn5dc7f4varbfkry64m</a> </span>
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Page 6454 of Mathematical Reviews Vol. , Issue 96k [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The restricted choice number c;(G) is defined in the same way as is the choice number c(G), except that there are only k 05 COMBINATORICS 6454 colors from which to form the lists on the vertices of G.  ...  The total chromatic number of a graph is the minimum number of colors needed to color the nodes and the edges of a graph in such a way that adjacent elements are colored differently.  ... 
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Linear Time Algorithm for Computing a Small Biclique in Graphs without Long Induced Paths [chapter]

Aistis Atminas, Vadim V. Lozin, Igor Razgon
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The biclique problem asks, given a graph G and a parameter k, whether G has a complete bipartite subgraph of k vertices in each part (a biclique of order k).  ...  In this paper we consider a restricted version of this problem by introducing an additional parameter s and assuming that G does not have induced (i.e. chordless) paths of length s.  ...  of the University of Bergen (hosted by Fedor Fomin).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31155-0_13">doi:10.1007/978-3-642-31155-0_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/omvcjx264ndjpjrdgaadlr645i">fatcat:omvcjx264ndjpjrdgaadlr645i</a> </span>
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Succinct Encodings of Graph Isomorphism [chapter]

Bireswar Das, Patrick Scharpfenecker, Jacobo Torán
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also give an algorithm for the DNF encoded version of GI whose running time depends only on the size of the succinct representation. * bireswar@iitgn.ac.in † patrick.scharpfenecker@uni-ulm.de, Supported  ...  We introduce a new way for encoding graph problems, based on CNF or DNF formulas.  ...  We check for all (exponentially many) nodes that 1) the intersection of colors of all biclique-sides it belongs to is not empty and 2) at least one of these colors is not used by any of the neighbouring  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-04921-2_23">doi:10.1007/978-3-319-04921-2_23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hs4quarecrgelc77d4ojd2hdhm">fatcat:hs4quarecrgelc77d4ojd2hdhm</a> </span>
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