منابع مشابه
Coloring Clean and K4-free Circle Graphs
A circle graph is the intersection graph of chords drawn in a circle. The best known general upper bound on the chromatic number of circle graphs with clique number k is 50 · 2. We prove a stronger bound of 2k − 1 for graphs in a simpler subclass of circle graphs, so called clean graphs. Based on this result we prove that the chromatic number of every circle graph with clique number at most 3 i...
متن کاملColoring (P6, diamond, K4)-free graphs
We show that every (P6, diamond, K4)-free graph is 6-colorable. Moreover, we give an example of a (P6, diamond, K4)-free graph G with χ(G) = 6. This generalizes some known results in the literature.
متن کاملOn r-hued coloring of K4-minor free graphs
A list assignment L of G is a mapping that assigns every vertex v ∈ V (G) a set L(v) of positive integers. For a given list assignment L of G, an (L, r)-coloring of G is a proper coloring c such that for any vertex v with degree d(v), c(v) ∈ L(v) and v is adjacent to at least min {d(v), r} different colors. The r-hued chromatic number of G, χr (G), is the least integer k such that for any v ∈ V...
متن کاملList-coloring graphs without K4, k-minors
In this note, it is shown that every graph with no K4,k-minor is 4k-list-colorable. We also give an extremal function for the existence for a K4,k-minor. Our proof implies that there is a linear time algorithm for showing that either G has a K4,k-minor or G is 4k-choosable. In fact, if the latter holds, then the algorithm gives rise to a 4k-list-coloring. © 2008 Elsevier B.V. All rights reserved.
متن کاملColoring precolored perfect graphs
We consider the question of the computational complexity of coloring perfect graphs with some precolored vertices. It is well known that a perfect graph can be colored optimally in polynomial time. Our results give a sharp border between the polynomial and NP-complete instances, when precolored vertices occur. The key result on the polynomially solvable cases includes a good characterization th...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1987
ISSN: 0095-8956
DOI: 10.1016/0095-8956(87)90048-7