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

2003
*
Random structures & algorithms (Print)
*

Fixing a graph G

doi:10.1002/rsa.10102
fatcat:ag4qwb3rkfbhxcatprqep5m7g4
*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. ...##
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Constrained path-finding and structure from acyclicity
[article]

2020
*
arXiv
*
pre-print

We show that trails avoiding forbidden transitions,

arXiv:1901.07028v2
fatcat:urwjyp44nrhlhb3uanfb4lk7bu
*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. ...##
###
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]

2016
*
arXiv
*
pre-print

The problem of finding

arXiv:1601.02271v2
fatcat:tr6aovdg7rakriatw4ghsuqj5a
*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. ...##
###
Rainbow graph splitting

2011
*
Theoretical Computer Science
*

Indeed,

doi:10.1016/j.tcs.2011.06.004
fatcat:h7revtz6gbd4nk66bkbbf4w32q
*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. ...##
###
Rainbow triangles in three-colored graphs

2017
*
Journal of combinatorial theory. Series B (Print)
*

Erdos

doi:10.1016/j.jctb.2017.04.002
fatcat:jz27uuw5i5ejnljthziogra73i
*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*. ...##
###
Approximate Hypergraph Coloring under Low-discrepancy and Related Promises
[article]

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. ...

##
###
Transversals in generalized Latin squares
[article]

2017
*
arXiv
*
pre-print

Akbari

arXiv:1701.08220v1
fatcat:hprucbkudbbnljbq33hptyl45e
*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*? ...##
###
Transversals in generalized Latin squares

2018
*
Ars Mathematica Contemporanea
*

Akbari

doi:10.26493/1855-3974.1316.2d2
fatcat:2htqy4amnredvbbxhahc3vydym
*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*? ...##
###
The b-Chromatic Number of Cubic Graphs

2010
*
Graphs and Combinatorics
*

We prove that a graph

doi:10.1007/s00373-010-0898-9
fatcat:5j4t3ji33bbopoker7veh5aybi
*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. ...##
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On the thinness and proper thinness of a graph
[article]

2018
*
arXiv
*
pre-print

thinness

arXiv:1704.00379v3
fatcat:23obd5fihffm7plusg4ikrvspy
*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. ...##
###
Pattern detection in large temporal graphs using algebraic fingerprints
[chapter]

2020
*
Proceedings of the 2020 SIAM International Conference on Data Mining
*

For example,

doi:10.1137/1.9781611976236.5
dblp:conf/sdm/ThejaswiG20
fatcat:tbljv2j56jb3riym674xncjxlu
*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. ...##
###
Minimum color‐degree perfect b ‐matchings

2020
*
Networks
*

Opening, plenary

doi:10.1002/net.21974
fatcat:4qgtutmxrrcy7anvxks4fivcii
*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 ...##
###
Finding path motifs in large temporal graphs using algebraic fingerprints
[article]

2020
*
arXiv
*
pre-print

For instance,

arXiv:2001.07158v4
fatcat:2a3rlkc5xfdiplcfgmerf5w3re
*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. ...##
###
Properly colored Hamilton cycles in Dirac-type hypergraphs
[article]

2020
*
arXiv
*
pre-print

For instance, we prove that if H is a k-uniform hypergraph

arXiv:2006.16544v1
fatcat:u74ydbdgsneyjl4chp6adub4pi
*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. ...
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