A reduction procedure for coloring perfect K4-free graphs
نویسندگان
چکیده
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 کاملK4-free Graphs as a Free Algebra
Graphs of treewidth at most two are the ones excluding the clique with four vertices (K4) as a minor, or equivalently, the graphs whose biconnected components are series-parallel. We turn those graphs into a finitely presented free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting these graphs: in addition ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1987
ISSN: 0095-8956
DOI: 10.1016/0095-8956(87)90019-0