Separating tree-chromatic number from path-chromatic number
نویسندگان
چکیده
منابع مشابه
Ramsey Theory for Binary Trees and the Separation of Tree-chromatic Number from Path-chromatic Number
We propose a Ramsey theory for binary trees and prove that for every r-coloring of “strong copies” of a small binary tree in a huge complete binary tree T , we can find a strong copy of a large complete binary tree in T with all small copies monochromatic. As an application, we construct a family of graphs which have treechromatic number at most 2 while the path-chromatic number is unbounded. T...
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Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (Xt : t ∈ V (T ))) such that G[Xt] has chromatic number at most k for each t ∈ V (T ). This seems to be a new concept, and this paper is a collection of observations on the topic. In particular we show that there are graphs with tree-chromatic number two and with arbitrarily large chromatic number; ...
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Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2019
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2019.02.003