Displaying similar documents to “A note on the chromatic number of the alternative negation of two graphs”

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)...

Edge colorings and total colorings of integer distance graphs

Arnfried Kemnitz, Massimiliano Marangio (2002)

Discussiones Mathematicae Graph Theory

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An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.

Ramseyan properties of graphs.

DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)

The Electronic Journal of Combinatorics [electronic only]

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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...

On multiset colorings of graphs

Futaba Okamoto, Ebrahim Salehi, Ping Zhang (2010)

Discussiones Mathematicae Graph Theory

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A vertex coloring of a graph G is a multiset coloring if the multisets of colors of the neighbors of every two adjacent vertices are different. The minimum k for which G has a multiset k-coloring is the multiset chromatic number χₘ(G) of G. For every graph G, χₘ(G) is bounded above by its chromatic number χ(G). The multiset chromatic numbers of regular graphs are investigated. It is shown that for every pair k, r of integers with 2 ≤ k ≤ r - 1, there exists an r-regular graph with multiset...

Note on enumeration of labeled split graphs

Vladislav Bína, Jiří Přibil (2015)

Commentationes Mathematicae Universitatis Carolinae

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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.

Light Graphs In Planar Graphs Of Large Girth

Peter Hudák, Mária Maceková, Tomáš Madaras, Pavol Široczki (2016)

Discussiones Mathematicae Graph Theory

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A graph H is defined to be light in a graph family 𝒢 if there exist finite numbers φ(H, 𝒢) and w(H, 𝒢) such that each G ∈ 𝒢 which contains H as a subgraph, also contains its isomorphic copy K with ΔG(K) ≤ φ(H, 𝒢) and ∑x∈V(K) degG(x) ≤ w(H, 𝒢). In this paper, we investigate light graphs in families of plane graphs of minimum degree 2 with prescribed girth and no adjacent 2-vertices, specifying several necessary conditions for their lightness and providing sharp bounds on φ and w...