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Local Anti-Ramsey Numbers of Graphs

2003
*
Combinatorics, probability & computing
*

We study properly coloured subgraphs and rainbow subgraphs forced in edge-colourings

doi:10.1017/s0963548303005868
fatcat:vfiyiaxec5hqnfx6vwj2wqyxdi
*of*complete*graphs*in which each vertex is incident to a large*number**of*colours. ... A subgraph H in an edge-colouring is properly coloured if incident edges*of*H are assigned different colours, and H is rainbow if no two edges*of*H are assigned the same colour. ... In this paper, we consider the*local*variation*of*the*anti*-*Ramsey*problem. ...##
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Online and size anti-Ramsey numbers

2014
*
Journal of Combinatorics
*

The smallest

doi:10.4310/joc.2014.v5.n1.a4
fatcat:e6lbgmq4cjbivmvcs5yn3yqcka
*number**of*edges in a*graph*any*of*whose proper edge colorings contains a totally multicolored copy*of*a*graph*H is the size*anti*-*Ramsey**number*ARs(H)*of*H. ... This*number*in offline and online setting is investigated here. ...*anti*-*Ramsey**number*AR s and*local**anti*-*Ramsey**number*AR loc . ...##
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Online and size anti-Ramsey numbers
[article]

2013
*
arXiv
*
pre-print

The smallest

arXiv:1311.0539v1
fatcat:k3djj2sidfeplamvkzsealxlya
*number**of*edges in a*graph*any*of*whose proper edge colorings contains a totally multicolored copy*of*a*graph*H is the size*anti*-*Ramsey**number*AR_s(H)*of*H. ... This*number*in offline and online setting is investigated here. ...*anti*-*Ramsey**number*AR s and*local**anti*-*Ramsey**number*AR loc . ...##
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Rainbow Generalizations of Ramsey Theory: A Survey

2010
*
Graphs and Combinatorics
*

In this work, we collect

doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
*Ramsey*-type results concerning rainbow and proper edge colorings*of**graphs*. Editions ... Within the class*of**graphs*in which each vertex is incident to many colors, the*anti*-*Ramsey*problem was studied in [18] under the title*of**local**anti*-*Ramsey**numbers*. ... The idea*of**anti*-*Ramsey**numbers*for cliques was extended in [27] to coloring in rounds. ...##
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Rainbow generalizations of Ramsey theory - a dynamic survey

2014
*
Theory and Applications of Graphs
*

In this work, we collect

doi:10.20429/tag.2014.000101
fatcat:zawfrrlt4jc4fbtiebsbpprsli
*Ramsey*-type results concerning rainbow edge colorings*of**graphs*. ... The authors*of*[68] also found the Gallai*Ramsey**numbers*for all trees*of*order at most 6. Regarding paths in general, the following represents the best known bounds. ... Acknowledgement The authors would like to thank Maria Axenovich, Tao Jiang and the referee for helpful comments and corrections on the initial publication*of*this work. ...##
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On degree anti-Ramsey numbers

2017
*
European journal of combinatorics (Print)
*

The degree

doi:10.1016/j.ejc.2016.09.002
fatcat:6e4cnp5cr5gfzlbvukseoh356a
*anti*-*Ramsey**number*AR_d(H)*of*a*graph*H is the smallest integer k for which there exists a*graph*G with maximum degree at most k such that any proper edge colouring*of*G yields a rainbow copy ... In this paper we prove a general upper bound on degree*anti*-*Ramsey**numbers*, determine the precise value*of*the degree*anti*-*Ramsey**number**of*any forest, and prove an upper bound on the degree*anti*-*Ramsey*...*Local**anti*-*Ramsey**numbers*are discussed in [3] as a special case*of*a broader notion. ...##
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Page 6741 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

Summary: “Certain generalizations

*of*the*Ramsey*and*anti*-*Ramsey**numbers*have been introduced and studied in the past few years. ... The rainbow*Ramsey**number*, also called the constrained*Ramsey**number*, RR(G,,G2)*of*two*graphs*G; and G> is the minimum integer N such that any edge-coloring*of*the complete*graph*Ky with any*number**of*...##
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Size and Degree Anti-Ramsey Numbers

2015
*
Graphs and Combinatorics
*

The size

doi:10.1007/s00373-015-1583-9
fatcat:szdb4aspvvh6rdlkw3ybbkf7cm
*anti*-*Ramsey**number**of*H, denoted by AR s (H), is the smallest*number**of*edges in a*graph*G such that any*of*its proper edge-colorings contains a rainbow copy*of*H. ... This settles a problem*of*Axenovich, Knauer, Stumpp and Ueckerdt. The proof is probabilistic and suggests the investigation*of*a related notion, which we call the degree*anti*-*Ramsey**number**of*a*graph*. ... Part*of*this work was done during the Japan Conference on*Graph*Theory and Combinatorics, which took place in Nihon University, Tokyo, in May, 2014. ...##
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Page 1720 of Mathematical Reviews Vol. 50, Issue 6
[page]

1975
*
Mathematical Reviews
*

Presia, A theorem on the theory

*of*the four-colour problem (pp. 1143-1148); G. B. Purdy, Planarity*of*two-point universal*graphs*(pp. 1149-1157); R. Rado,”*Anti*-*Ramsey*theorems (pp. ... Sds,*Anti*-*Ramsey*theorems (pp. 633-643); E. Etourneau, Existence and connectivity*of*planar*graphs*having 12 vertices*of*degree 5 and n-12 vertices*of*degree 6 (pp. 645-655); R. J. Faudree and R. H. ...##
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Rainbows in the Hypercube

2007
*
Graphs and Combinatorics
*

In this paper we start the investigation

doi:10.1007/s00373-007-0691-6
fatcat:lfxfp43fbjfgnexi54wmo5ediq
*of*this*anti*-*Ramsey*problem by providing bounds on f (Q n , Q k ) which are asymptotically tight for k = 2 and by giving some exact results. ... An edge coloring*of*a*graph*H is called rainbow if no two edges*of*H have the same color. ... There is a*number**of*results on*anti*-*Ramsey**numbers*under different*local*constraints and on*anti*-*Ramsey**numbers**of*the structures other than*graphs*, such as posets, integers and so on. ...##
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Contents

2007
*
Discrete Mathematics
*

Huang
New upper bound formulas with parameters for

doi:10.1016/s0012-365x(07)00008-8
fatcat:g2ns66lzezewzfytkhjrr6tasq
*Ramsey**numbers*760 K.-I. Kawarabayashi and A. ... Wanke A*local*characterization*of*bounded clique-width for line*graphs*756 Y. Huang, Y. Wang, W. Sheng, J. Yang, K. Zhang and J. ...##
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Turán's Theorem in the Hypercube

2007
*
SIAM Journal on Discrete Mathematics
*

A relationship to

doi:10.1137/060649422
fatcat:lfyj6vsafzhtji6jfwe4haboke
*anti*-*Ramsey*colorings is also discussed. We discover much less about the Turán-type question which motivated our investigations. Numerous problems and conjectures are raised. ... The*number**of*colors is tight up to a constant factor, as it turns out that a similar coloring with d+1 2 + 1 colors is not possible. The corresponding question for vertices is also considered. ... A coloring c*of*the edges*of**graph*G is called H-*anti*-*Ramsey*if the restriction*of*c to any subgraph H 0 ⊆ G, H 0 ∼ = H, is not rainbow. ...##
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Page 2850 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

The authors determine the reduced

*Ramsey**numbers**of*the ten*graphs**of*order four or less with no isolates. ... Mader (Hannover) Babai, Laszlé6 (H-EOTVO-A) 86g:05063 An*anti*-*Ramsey*theorem.*Graphs*Combin. 1 (1985), no. 1, 23-28. ...##
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On Homomorphism Graphs
[article]

2021
*
arXiv
*
pre-print

In particular, we show that for Δ>2 it is impossible to give a simple characterization

arXiv:2111.03683v1
fatcat:exhbxopan5e6hauam365k7ww5i
*of*acyclic Δ-regular Borel*graphs*with Borel chromatic*number*at most Δ: such*graphs*form a Σ^1_2-complete set. ... The motivation for the construction comes from the adaptation*of*this method to the*LOCAL*model*of*distributed computing. ... Let us denote by χ wpr−∆ 1 2 (H) the weakly provably ∆ 1 2 -chromatic*number**of*H (see Section 2). Theorem 1.1. Let H be a*locally*countable Borel*graph*. ...##
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Ramsey games

2002
*
Discrete Mathematics
*

This is a partly survey, partly new results paper about

doi:10.1016/s0012-365x(01)00224-2
fatcat:ty6tqyllong6hcy65yvbrblwvi
*Ramsey*games.*Ramsey*games belong to the wider class*of*positional games. ... In Section 1 we brie y recall the basic concepts and results*of*positional games in general, and apply them to the particular case*of**Ramsey*games. ...*Ramsey**Graph*Game The board*of*the game is the complete*graph*K s with s vertices. ...
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