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Local Anti-Ramsey Numbers of Graphs
2003
Combinatorics, probability & computing
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We study properly coloured subgraphs and rainbow subgraphs forced in edge-colourings 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. ...
doi:10.1017/s0963548303005868
fatcat:vfiyiaxec5hqnfx6vwj2wqyxdi
Online and size anti-Ramsey numbers
2014
Journal of Combinatorics
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The smallest 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 . ...
doi:10.4310/joc.2014.v5.n1.a4
fatcat:e6lbgmq4cjbivmvcs5yn3yqcka
Online and size anti-Ramsey numbers
[article]
2013
arXiv
pre-print
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The smallest 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 . ...
arXiv:1311.0539v1
fatcat:k3djj2sidfeplamvkzsealxlya
Rainbow Generalizations of Ramsey Theory: A Survey
2010
Graphs and Combinatorics
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In this work, we collect 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. ...
doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
Rainbow generalizations of Ramsey theory - a dynamic survey
2014
Theory and Applications of Graphs
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In this work, we collect 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. ...
doi:10.20429/tag.2014.000101
fatcat:zawfrrlt4jc4fbtiebsbpprsli
On degree anti-Ramsey numbers
2017
European journal of combinatorics (Print)
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2015 pre-print arXiv:1507.07381v1 fatcat:ze53jf5igbhnher3jijkhyiu5q
The degree 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. ...
doi:10.1016/j.ejc.2016.09.002
fatcat:6e4cnp5cr5gfzlbvukseoh356a
Page 6741 of Mathematical Reviews Vol. , Issue 2004i
[page]
2004
Mathematical Reviews
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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 ...
Size and Degree Anti-Ramsey Numbers
2015
Graphs and Combinatorics
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The size 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. ...
doi:10.1007/s00373-015-1583-9
fatcat:szdb4aspvvh6rdlkw3ybbkf7cm
Page 1720 of Mathematical Reviews Vol. 50, Issue 6
[page]
1975
Mathematical Reviews
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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. ...
Rainbows in the Hypercube
2007
Graphs and Combinatorics
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In this paper we start the investigation 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. ...
doi:10.1007/s00373-007-0691-6
fatcat:lfxfp43fbjfgnexi54wmo5ediq
Contents
2007
Discrete Mathematics
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Huang
New upper bound formulas with parameters for 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. ...
doi:10.1016/s0012-365x(07)00008-8
fatcat:g2ns66lzezewzfytkhjrr6tasq
Turán's Theorem in the Hypercube
2007
SIAM Journal on Discrete Mathematics
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A relationship to 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. ...
doi:10.1137/060649422
fatcat:lfyj6vsafzhtji6jfwe4haboke
Page 2850 of Mathematical Reviews Vol. , Issue 86g
[page]
1986
Mathematical Reviews
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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. ...
On Homomorphism Graphs
[article]
2021
arXiv
pre-print
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In particular, we show that for Δ>2 it is impossible to give a simple characterization 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. ...
arXiv:2111.03683v1
fatcat:exhbxopan5e6hauam365k7ww5i
Ramsey games
2002
Discrete Mathematics
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This is a partly survey, partly new results paper about 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. ...
doi:10.1016/s0012-365x(01)00224-2
fatcat:ty6tqyllong6hcy65yvbrblwvi
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