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Bipartite almost distance-hereditary graphs

Méziane Aïder
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
In this paper, we define the class of bipartite almost distance-hereditary graphs (an increase of the distance by two is allowed by induced subgraphs) and obtain a characterization in terms of forbidden  ...  The notion of distance-heredity in graphs has been extended to construct the class of almost distance-hereditary graphs (an increase of the distance by one unit is allowed by induced subgraphs).  ...  almost distance hereditary graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disc.2007.07.038">doi:10.1016/j.disc.2007.07.038</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ncgs2j6ymbh3nfgigdyfzt5g5i">fatcat:ncgs2j6ymbh3nfgigdyfzt5g5i</a> </span>
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Page 4781 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</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;
Moreover, we characterize those chordal, distance- hereditary and HHD-free graphs by forbidden isometric subgraphs for which any LexBFS-ordering of the graph is a common perfect  ...  We show that any LexBFS-ordering of a chordal graph is a common perfect elimination ordering of all odd powers of this graph, and any LexBFS-ordering of a distance-hereditary graph is a common perfect  ... 
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Almost distance-hereditary graphs

Méziane Aı̈der
<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;
In this paper, we extend the notion of distance-hereditary graphs by introducing the class of almost distance-hereditary graphs (a very weak increase of the distance is allowed by induced subgraphs).  ...  Distance-hereditary graphs (graphs in which the distances are preserved by induced subgraphs) have been introduced and characterized by Howorka.  ...  Structure of almost distance-hereditary graphs The vertices of an almost distance-hereditary graph can be partitioned in two subsets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(00)00401-5">doi:10.1016/s0012-365x(00)00401-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4krevbt3grdxhnxfprc444qyd4">fatcat:4krevbt3grdxhnxfprc444qyd4</a> </span>
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Page 7840 of Mathematical Reviews Vol. , Issue 2002K [page]

<span title="">2002</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;
A graph G = (V, E) is almost distance-hereditary if for all connected induced subgraphs H = (V*, E*) of G and for each pair of vertices u,v € V* the distance of u,v in H is at most the distance of u,v  ...  We also obtain some corollaries of this theorem.” 05 COMBINATORICS 2002k:05202 05C75 05C12 Aider, Méziane (DZ-BOUM; Algiers) Almost distance-hereditary graphs.  ... 
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Critical properties of bipartite permutation graphs [article]

Bogdan Alecu, Vadim Lozin, Dmitriy Malyshev
<span title="2020-10-27">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The class of bipartite permutation graphs enjoys many nice and important properties.  ...  In the present paper we identify critical subclasses of bipartite permutation graphs of various types.  ...  Then X is a minimal hereditary class with speed at least the Bell number if and only if there exists a finite graph K with loops allowed and an infinite almost periodic word w over V (K) such that X =  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.14467v1">arXiv:2010.14467v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4limdlsygvdatfeyksncg3bm2u">fatcat:4limdlsygvdatfeyksncg3bm2u</a> </span>
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Contents

<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Stern The k-edge intersection graphs of paths in a tree 451 E. Korach, U.N. Peled and U. Rotics Equistable distance-hereditary graphs 462 V.E. Levit and E.  ...  Rosenfeld The circuit polynomial of the restricted rooted product GðÀÞ of graphs with a bipartite core G 500 doi:10.1016/S0166-218X(08)00018-8  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-218x(08)00018-8">doi:10.1016/s0166-218x(08)00018-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jd6ycxxgnra5thguj7hxjpb5lq">fatcat:jd6ycxxgnra5thguj7hxjpb5lq</a> </span>
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Testing Odd-Cycle-Freeness in Boolean Functions [chapter]

Arnab Bhattacharyya, Elena Grigorescu, Prasad Raghavendra, Asaf Shapira
<span title="2012-01-17">2012</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
We show a black-box reduction from testing odd-cycle-freeness to testing bipartiteness of graphs. Such reductions have been shown previously (Král-Serra-Vena, Israel J.  ...  The first issue we study is directly reducing testing of linear-invariant properties of Boolean functions to testing associated graph properties.  ...  In order to obtain Theorem 5, observe that by Corollary 13, the distance to OCF for a function f is exactly double the distance to bipartiteness for the graph G(f ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973099.90">doi:10.1137/1.9781611973099.90</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/BhattacharyyaGRS12.html">dblp:conf/soda/BhattacharyyaGRS12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6dv6b7a5ojh7jcbqt3vyro4vle">fatcat:6dv6b7a5ojh7jcbqt3vyro4vle</a> </span>
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Testing Odd-Cycle-Freeness in Boolean Functions

ARNAB BHATTACHARYYA, ELENA GRIGORESCU, PRASAD RAGHAVENDRA, ASAF SHAPIRA
<span title="2012-08-10">2012</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/domxx2wewzae3e2m2ziqaqbyhm" style="color: black;">Combinatorics, probability &amp; computing</a> </i> &nbsp;
We show a black-box reduction from testing odd-cycle-freeness to testing bipartiteness of graphs. Such reductions have been shown previously (Král-Serra-Vena, Israel J.  ...  The first issue we study is directly reducing testing of linear-invariant properties of Boolean functions to testing associated graph properties.  ...  In order to obtain Theorem 5, observe that by Corollary 13, the distance to OCF for a function f is exactly double the distance to bipartiteness for the graph G(f ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0963548312000363">doi:10.1017/s0963548312000363</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/msikzqx5qnagpl4hkjrstfu7oi">fatcat:msikzqx5qnagpl4hkjrstfu7oi</a> </span>
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Local Graph Exploration and Fast Property Testing [chapter]

Artur Czumaj
<span title="">2010</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;
We will present some recent results about testing graph properties in sparse graphs and will discuss graph exploration techniques which allow very efficient algorithms for testing graph properties.  ...  [18] show also how to apply similar techniques to not only test graph properties, but also to approximate the distance to almost any hereditary property in any bounded degree hereditary families of  ...  For example, they show that if the underlying graph is planar, then any hereditary graph property (e.g., bipartiteness, k-colorability, or perfectness) is testable in time independent of the input size  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-15775-2_35">doi:10.1007/978-3-642-15775-2_35</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xiimnh663nd4phyun7bjzn3uzi">fatcat:xiimnh663nd4phyun7bjzn3uzi</a> </span>
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Page 4074 of Mathematical Reviews Vol. , Issue 97G [page]

<span title="">1997</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;
In this pa- per powers of distance-hereditary graphs are characterized. They are almost distance-hereditary in the sense that in powers 4-fans may occur, but not the other subgraphs listed above.  ...  A connected graph is distance-hereditary if each induced path is a shortest path. E. Howorka [Quart. J. Math.  ... 
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Hardness of edge-modification problems

Noga Alon, Uri Stav
<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;
In addition, we state a conjecture on the hardness of computing the edit distance from being induced H-free for any forbidden graph H.  ...  Namely, what is the edit distance ∆(G, P ) of a graph G from satisfying P ? Clearly, the computational complexity of such a problem strongly depends on P .  ...  Nevertheless, it can be observed that in almost all the applications, the focus is on graph properties that are hereditary, namely closed under removal of vertices (equivalently, closed under taking induced  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2009.07.002">doi:10.1016/j.tcs.2009.07.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hoywleu54beptelo3dikrzjo3a">fatcat:hoywleu54beptelo3dikrzjo3a</a> </span>
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Regularity partitions and the topology of graphons [article]

László Lovász, Balázs Szegedy
<span title="2010-02-23">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs.  ...  So a bipartite graph becomes a bigraph if we fix a bipartition and specify which bipartition class is first and second.  ...  Clearly, I(W ) is a hereditary graph property. Let P be a hereditary property of graphs. Then ∪ W ∈P I(W ) ⊆ P. (8) Indeed, if F / ∈ P, then t ind (F, G) = 0 for every G ∈ P, since P is hereditary.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1002.4377v1">arXiv:1002.4377v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mxbxbahnmbbg7dktyzcndeicge">fatcat:mxbxbahnmbbg7dktyzcndeicge</a> </span>
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Requiring chords in cycles

Terry A. McKee
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
This result generalizes to having or not having crossing chords and to having strong chords, with similar characterizations of a variety of graph classes that includes chordal bipartite, distance-hereditary  ...  , and strongly chordal graphs.  ...  A graph G is a distance-hereditary graph [1, 6] whenever the distance between two vertices in a connected induced subgraph always equals their distance in the full graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disc.2005.04.009">doi:10.1016/j.disc.2005.04.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iaxkg4zl4zevxo6t65ajj2h4i4">fatcat:iaxkg4zl4zevxo6t65ajj2h4i4</a> </span>
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An attractive class of bipartite graphs

Rodica Boliac, Vadim Lozin
<span title="">2001</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g64zvtslcjdqncvrfbmvf422qi" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs.  ...  We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.  ...  Nevertheless, efficient methods for jump-minimization have been found for several subclasses of bipartite graphs, like bipartite permutation [10] , biconvex [2] , convex [5] and distance-hereditary  ... 
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<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Thuillier, New classes of perfectly orderable graphs (1-3) 95}109 Fronc\ ek, D., Self-complementary factors of almost complete tripartite graphs of even order (1-3) 111}122 Frydrych, W., Nonhamiltonian  ...  MihoH k, On graphs with a local hereditary property (1-3) 53} 58 Delorme, C., Presentations of groups generated by transpositions (1-3) 59} 64  ... 
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