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Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints

Noga Alon, Tao Jiang, Zevi Miller, Dan Pritikin
2003 Random structures & algorithms (Print)  
Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every m-good edge-coloring of K n yields a properly edge-colored copy of G, and let g(m, G) denote the smallest n  ...  In particular, we show that for fixed m and d, and all sufficiently large n compared to m and d, f(m, G) ϭ n for all graphs G with n vertices and maximum degree at most d.  ...  For the remaining edges, which are PROPERLY COLORED SUBGRAPHS AND RAINBOW GRAPHS edges with both endpoints in the same subset A i , we assign them a new color ␣ not used in c.  ... 
doi:10.1002/rsa.10102 fatcat:ag4qwb3rkfbhxcatprqep5m7g4

Constrained path-finding and structure from acyclicity [article]

Lê Thành Dũng Nguyên
2020 arXiv   pre-print
We show that trails avoiding forbidden transitions, properly arc-colored directed trails and rainbow paths for complete multipartite color classes can be found in linear time, whereas finding rainbow paths  ...  Another result on graphs equipped with unique perfect matchings that we prove here is the combinatorial counterpart of a theorem due to Bellin in linear logic: a connection between blossoms and bridge  ...  A color class in an edge-colored graph is the set of all edges with some common color; it may also refer to the subgraph edge-induced by such a set.  ... 
arXiv:1901.07028v2 fatcat:urwjyp44nrhlhb3uanfb4lk7bu

Page 6741 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
colored subgraphs and rainbow subgraphs in edge-colorings with local constraints.  ...  Let f(m,G) be the smallest positive integer n such that every m-good edge-coloring of K,, (the complete graph with 7 vertices) yields a properly edge- colored copy of G, and let g(m, G) be the smallest  ... 

Bounded colorings of multipartite graphs and hypergraphs [article]

Nina Kamčev, Benny Sudakov, Jan Volec
2016 arXiv   pre-print
The problem of finding properly colored and rainbow Hamilton cycles in c was initiated in 1976 by Bollobás and Erdős and has been extensively studied since then.  ...  We generalize these results, giving sufficient local (resp. global) restrictions on the colorings which guarantee a properly colored (resp. rainbow) copy of a given hypergraph G.  ...  The authors would like to thank Oriol Serra for fruitful discussions on the topics related to this project and pointing out the references [6] and [19] to us.  ... 
arXiv:1601.02271v2 fatcat:tr6aovdg7rakriatw4ghsuqj5a

Rainbow graph splitting

A. Monti, B. Sinaimeri
2011 Theoretical Computer Science  
Indeed, in this case the induced subgraph has no edges, so we consider it being of an arbitrary color.  ...  In this paper we study the computational complexity of the following problem: Rainbow c-Splitting Problem Instance: An edge-colored graph G. Question: Is G rainbow c-splittable?  ...  Acknowledgements We would like to thank Riccardo Silvestri and an anonymous referee whose comments and suggestions helped to improve the quality of this paper.  ... 
doi:10.1016/j.tcs.2011.06.004 fatcat:h7revtz6gbd4nk66bkbbf4w32q

Rainbow triangles in three-colored graphs

József Balogh, Ping Hu, Bernard Lidický, Florian Pfender, Jan Volec, Michael Young
2017 Journal of combinatorial theory. Series B (Print)  
Erdos and Sos proposed a problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices.  ...  These results imply that lim F(n) n^3/6 = 0.4, and determine the unique limit object. In the proof we use flag algebras combined with stability arguments.  ...  Introduction An edge-coloring of a graph (or a subgraph of a graph) is rainbow if each of its edges has a different color.  ... 
doi:10.1016/j.jctb.2017.04.002 fatcat:jz27uuw5i5ejnljthziogra73i

Approximate Hypergraph Coloring under Low-discrepancy and Related Promises [article]

Vijay V. S. P. Bhattiprolu, Venkatesan Guruswami, Euiwoong Lee
2015 arXiv   pre-print
In this work, we study the complexity of approximate hypergraph coloring, for both the maximization (finding a 2-coloring with fewest miscolored edges) and minimization (finding a proper coloring using  ...  and the best algorithms to color the hypergraph properly require ≈ n^1-1/k colors, approaching the trivial bound of n as k increases.  ...  Thus we can properly 2-color F in polynomial time. Theorem 4. 8 . 8 Let H = V, E ⊆ V k be a k-uniform (k − 1)-rainbow colorable hypergraph with n vertices.  ... 
arXiv:1506.06444v1 fatcat:wipfawarkjex5ic4qmb4weovaa

Transversals in generalized Latin squares [article]

János Barát, Zoltán Lóránt Nagy
2017 arXiv   pre-print
Akbari and Alipour defined l(n) as the least integer such that every properly edge-colored K_n,n, which contains at least l(n) different colors, admits a multicolored perfect matching.  ...  We propose a conjecture related to a well-known result by Woolbright and Fu, that every proper edge-coloring of K_2n admits a multicolored 1-factor.  ...  What is the least number of colors t(n, 2), which guarantees a rainbow 2-factor subgraph on at least n − 1 vertices in a properly edge-colored complete graph K n colored by at least t(n, 2) colors?  ... 
arXiv:1701.08220v1 fatcat:hprucbkudbbnljbq33hptyl45e

Transversals in generalized Latin squares

János Barát, Zoltán Lóránt Nagy
2018 Ars Mathematica Contemporanea  
Akbari and Alipour defined l(n) as the least integer such that every properly edge-colored K n,n , which contains at least l(n) different colors, admits a multicolored perfect matching.  ...  We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order n is equivalent to a proper edge-coloring of K n,n .  ...  What is the least number of colors t(n, 2), which guarantees a rainbow 2-factor subgraph on at least n − 1 vertices in a properly edge-colored complete graph K n colored by at least t(n, 2) colors?  ... 
doi:10.26493/1855-3974.1316.2d2 fatcat:2htqy4amnredvbbxhahc3vydym

The b-Chromatic Number of Cubic Graphs

Marko Jakovac, Sandi Klavžar
2010 Graphs and Combinatorics  
We prove that a graph with every edge belonging to at most c cycles has game coloring number of at most c + 4.  ...  This generalises recent result [1] that for any cactus G (a graph with edge-disjoint cycles) col g (G) ≤ 5. Keywords: game chromatic number, game coloring number. AMS Subject Classication: 05C15.  ...  Keywords: induced subgraph; edge coloring; Cartesian product.  ... 
doi:10.1007/s00373-010-0898-9 fatcat:5j4t3ji33bbopoker7veh5aybi

On the thinness and proper thinness of a graph [article]

Flavia Bonomo, Diego de Estrada
2018 arXiv   pre-print
thinness with other graph invariants in the literature.  ...  Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs.  ...  to us, and Yuri Faenza for his valuable help in the improvement of the manuscript.  ... 
arXiv:1704.00379v3 fatcat:23obd5fihffm7plusg4ikrvspy

Pattern detection in large temporal graphs using algebraic fingerprints [chapter]

Suhas Thejaswi, Aristides Gionis
2020 Proceedings of the 2020 SIAM International Conference on Data Mining  
For example, in a real-world graph dataset with more than six million edges and a multi-set query with ten colors, we can extract an optimal solution in less than eight minutes on a haswell desktop with  ...  In particular, given a vertex-colored temporal graph and a multi-set of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query.  ...  Rainbow path problem in temporal graphs.  ... 
doi:10.1137/1.9781611976236.5 dblp:conf/sdm/ThejaswiG20 fatcat:tbljv2j56jb3riym674xncjxlu

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
Opening, plenary and closing sessions will take place in the PP amphitheatre. The cocktail event on Tuesday evening will take place in the salle des textiles room, located in Access 3, 1st floor.  ...  then possibly someone will ask a question just to fill in the horrible silence, and then other questions may follow.  ...  The benchmark we consider consists in the standard MultiStart (MS) Algorithm, in which a starting point is randomly generated and a local algorithm, i.e., a procedure producing solutions with local optimal  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii

Finding path motifs in large temporal graphs using algebraic fingerprints [article]

Suhas Thejaswi, Aristides Gionis, Juho Lauri
2020 arXiv   pre-print
For instance, in a real-world graph dataset with more than six million edges and a multiset query with ten colors, we can extract an optimum solution in less than eight minutes on a Haswell desktop with  ...  We demonstrate that our solution scales to massive graphs with up to a billion edges for a multiset query with five colors and up to hundred million edges for a multiset query with ten colors, despite  ...  Systems and Software Program (WASP) funded by Knut and Alice Wallenberg Foundation.  ... 
arXiv:2001.07158v4 fatcat:2a3rlkc5xfdiplcfgmerf5w3re

Properly colored Hamilton cycles in Dirac-type hypergraphs [article]

Sylwia Antoniuk, Nina Kamčev, Andrzej Ruciński
2020 arXiv   pre-print
For instance, we prove that if H is a k-uniform hypergraph with minimum codegree at least (1/2 + γ )n, γ >0, and n is sufficiently large, then any edge coloring ϕ satisfying appropriate local constraints  ...  yields a properly colored tight Hamilton cycle in H.  ...  terms of rainbow subgraphs, such as Latin transversals.  ... 
arXiv:2006.16544v1 fatcat:u74ydbdgsneyjl4chp6adub4pi
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