Results 241 to 250 of about 11,475 (265)

The clique-perfectness and clique-coloring of outer-planar graphs

Journal of Combinatorial Optimization, 2019
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Zuosong Liang, Erfang Shan, Liying Kang
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Complexity of clique‐coloring odd‐hole‐free graphs

Journal of Graph Theory, 2009
AbstractIn this paper we investigate the problem of clique‐coloring, which consists in coloring the vertices of a graph in such a way that no monochromatic maximal clique appears, and we focus on odd‐hole‐free graphs. On the one hand we do not know any odd‐hole‐free graph that is not 3‐clique‐colorable, but on the other hand it is NP‐hard to decide if ...
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Coloring the Maximal Cliques of Graphs

SIAM Journal on Discrete Mathematics, 2004
Summary: We are concerned with the so-called clique-colorations of a graph, that is, colorations of the vertices so that no maximal clique is monochromatic. On one hand, it is known to be NP-complete to decide whether a perfect graph is 2-clique-colorable, or whether a triangle-free graph is 3-clique-colorable; on the other hand, there is no example of
Bacsó, Gábor, Gravier, Sylvain, Gyárfás, András, Preissmann, Myriam, Sebo, András   +4 more
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NOTE - Edge-Coloring Cliques with Many Colors on Subcliques

Combinatorica, 2000
\textit{D. Mubayi} [Combinatorica 18, No. 2, 293-296 (1998; Zbl 0910.05035)] constructed a coloring of \(E(K_N)\) with \(e^{O(\sqrt{\log n})}\) colors in which the edges of every copy of \(K_4\) get together at least three colors. It is shown in this paper that this construction has also the property that the edges of every copy of \(K_p\) get together
Eichhorn, Dennis, Mubayi, Dhruv
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Note – Edge-Coloring Cliques with Three Colors on All 4-Cliques

COMBINATORICA, 1998
For integers \(n,p\) and \(q\), a \((p,q)\)-coloring of \(K_n\) is a coloring of the edges of \(K_n\) in which the edges of every \(p\)-cligue together receive at least \(q\) colors. Let \(f(n,p,q)\) denote the minimum number of colors in a \((p,q)\)-coloring of \(K_n\). The author proves that \(f(n,4,3)
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Maximum Colorful Cliques in Vertex-Colored Graphs

2018
In this paper we study the problem of finding a maximum colorful clique in vertex-colored graphs. Specifically, given a graph with colored vertices, we wish to find a clique containing the maximum number of colors. Note that this problem is harder than the maximum clique problem, which can be obtained as a special case when each vertex has a different ...
Italiano, Giuseppe, Manoussakis, Yannis, Nguyen, Kim Thang, Pham, Hong-Phong   +3 more
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Coloring Clique‐free Graphs in Linear Expected Time

Random Structures & Algorithms, 1992
AbstractThis article presents a linear expected time algorithm to color every graph which does not contain a clique on l + 1 vertices as a subgraph with a minimal number of colors. This extends a result of Dyer and Frieze for l‐colorable graphs. For the proof we develop a new method which allows us to precisely estimate the number of graphs with ...
Prömel, Hans Jürgen, Steger, Angelika
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Acyclic Coloring Parameterized by Directed Clique-Width

2021
An acyclic r-coloring of a directed graph \(G=(V,E)\) is a partition of the vertex set V into r acyclic sets. The dichromatic number of a directed graph G is the smallest r such that G allows an acyclic r-coloring. For symmetric digraphs the dichromatic number equals the well-known chromatic number of the underlying undirected graph.
Frank Gurski, Dominique Komander, Carolin Rehs   +2 more
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Cliques, holes and the vertex coloring polytope

Information Processing Letters, 2004
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Campêlo, Manoel, Corrêa, Ricardo, Frota, Yuri   +2 more
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Clique-Colorings of Graphs

In this dissertation, we study the clique-chromatic numbers of graphs. We obtain the exact values of the clique-chromatic numbers of the line graphs of complete graphs and a characterization of the clique-chromatic numbers of the line graphs of triangle-free graphs. We improve bounds of the clique-chromatic number of the family of F-free graphs when F =
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