Results 1 to 10 of about 11,381 (177)
Iterated Clique Reductions in Vertex Weighted Coloring for Large Sparse Graphs [PDF]
Entropy, 2023 The Minimum Vertex Weighted Coloring (MinVWC) problem is an important generalization of the classic Minimum Vertex Coloring (MinVC) problem which is NP-hard. Given a simple undirected graph G=(V,E), the MinVC problem is to find a coloring s.t.
Yi Fan +7 more
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Optimal (Degree+1)-Coloring in Congested Clique [PDF]
, 2023 27 pages.
Sam Coy +3 more
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b-Coloring Parameterized by Clique-Width [PDF]
Theory of Computing Systems, 2023 AbstractWe provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva (Algorithmica 80(1), 104–115, 2018) and Bonomo et al. (Graphs and Combinatorics 25(2), 153–167, 2009). This
Lars Jaffke +2 more
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Clique-Coloring of $$K_{3,3}$$-Minor Free Graphs [PDF]
Bulletin of the Iranian Mathematical Society, 2019 13 pages, 2 ...
Behnaz Omoomi, Maryam Taleb
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On Nordhaus-Gaddum type relations of δ-complement graphs [PDF]
Heliyon, 2023 The δ-complement graphs were introduced by Amrithalakshmi et al. in 2022. In their work, some interesting properties of the graphs such as δ-self-complementary, adjacency, and hamiltonicity were studied.
Panupong Vichitkunakorn +2 more
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Crossings, Colorings, and Cliques [PDF]
The Electronic Journal of Combinatorics, 2009 Albertson conjectured that if graph $G$ has chromatic number $r$, then the crossing number of $G$ is at least that of the complete graph $K_r$. This conjecture in the case $r=5$ is equivalent to the four color theorem. It was verified for $r=6$ by Oporowski and Zhao. In this paper, we prove the conjecture for $7 \leq r \leq 12$ using results of Dirac;
Michael O. Albertson +2 more
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Clique-Relaxed Graph Coloring [PDF]
Involve, a Journal of Mathematics, 2011 We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs.
Dunn, Charles +5 more
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Structural Parameterizations of Clique Coloring [PDF]
Algorithmica, 2021 AbstractA clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed $$q \ge 2$$ q
Lars Jaffke +2 more
openalex +7 more sources
An exact algorithm to find a maximum weight clique in a weighted undirected graph [PDF]
Scientific ReportsWe introduce a new algorithm MaxCliqueWeight for identifying a maximum weight clique in a weighted graph, and its variant MaxCliqueDynWeight with dynamically varying bounds.
Kati Rozman +3 more
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Clique-Relaxed Competitive Graph Coloring [PDF]
, 2014 We investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color is legal for a vertex if said vertex has no neighbors colored .
Michel Alexis +3 more
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