The rank of a cograph.
Royle, Gordon F. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “More counterexamples to the Alon-Saks-Seymour and rank-coloring conjectures.”
The rank of a cograph.
On the function “sandwiched" between and .
Dobrynin, V.Y. (1997)
The Electronic Journal of Combinatorics [electronic only]
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Nonrepetitive colorings of graphs -- a survey.
Grytczuk, Jarosław (2007)
International Journal of Mathematics and Mathematical Sciences
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A strengthening of Brooks' Theorem for line graphs.
Rabern, Landon (2011)
The Electronic Journal of Combinatorics [electronic only]
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Trivial Selmer groups and even partitions of a graph.
Brown, Morgan V., Calkin, Neil J., James, Kevin, King, Adam J., Lockard, Shannon, Rhoades, Robert C. (2006)
Integers
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Equitable coloring of Kneser graphs
Robert Fidytek, Hanna Furmańczyk, Paweł Żyliński (2009)
Discussiones Mathematicae Graph Theory
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The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,...,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k)...
On some problems in combinatorial set theory.
Erdős, Paul (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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Crossings, colorings, and cliques.
Albertson, Michael O., Cranston, Daniel W., Fox, Jacob (2009)
The Electronic Journal of Combinatorics [electronic only]
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Circular chromatic number of planar graphs of large odd girth.
Zhu, Xuding (2001)
The Electronic Journal of Combinatorics [electronic only]
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A survey of minimum saturated graphs.
Faudree, Jill R., Faudree, Ralph J., Schmitt, John R. (2011)
The Electronic Journal of Combinatorics [electronic only]
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An extremal property of Turán graphs.
Lazebnik, Felix, Tofts, Spencer (2010)
The Electronic Journal of Combinatorics [electronic only]
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Precoloring extension. II. Graphs classes related to bipartite graphs.
Hujter, M., Tuza, Zs. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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Equitable Colorings Of Corona Multiproducts Of Graphs
Hanna Furmánczyk, Marek Kubale, Vahan V. Mkrtchyan (2017)
Discussiones Mathematicae Graph Theory
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A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is known that the problem of computation of 𝜒=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts...
Upper and lower bounds for .
Xu, Xiaodong, Luo, Haipeng, Shao, Zehui (2010)
The Electronic Journal of Combinatorics [electronic only]
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On 1-dependent ramsey numbers for graphs
E.J. Cockayne, C.M. Mynhardt (1999)
Discussiones Mathematicae Graph Theory
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A set X of vertices of a graph G is said to be 1-dependent if the subgraph of G induced by X has maximum degree one. The 1-dependent Ramsey number t₁(l,m) is the smallest integer n such that for any 2-edge colouring (R,B) of Kₙ, the spanning subgraph B of Kₙ has a 1-dependent set of size l or the subgraph R has a 1-dependent set of size m. The 2-edge colouring (R,B) is a t₁(l,m) Ramsey colouring of Kₙ if B (R, respectively) does not contain a 1-dependent set of size l (m, respectively);...