منابع مشابه
Linear choosability of sparse graphs
A linear coloring is a proper coloring such that each pair of color classes induces a union of disjoint paths. We study the linear list chromatic number, denoted lcl(G), of sparse graphs. The maximum average degree of a graph G, denoted mad(G), is the maximum of the average degrees of all subgraphs of G. It is clear that any graph Gwithmaximumdegree ∆(G) satisfies lcl(G) ≥ ⌈∆(G)/2⌉ + 1. In this...
متن کاملLinear choosability of graphs
A proper vertex coloring of a non oriented graph G = (V, E) is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph G is L-list colorable if for a given list assignment L = {L(v) : v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is L-list colorable for every list assignment with |L(v)| ≥ k for all v ∈ V , then G...
متن کاملAdaptable choosability of planar graphs with sparse short cycles
Given a (possibly improper) edge-colouring F of a graph G, a vertex colouring of G is adapted to F if no colour appears at the same time on an edge and on its two endpoints. A graph G is called adaptably k-choosable (for some positive integer k) if for any list assignment L to the vertices of G, with |L(v)| ≥ k for all v, and any edge-colouring F of G, G admits a colouring c adapted to F where ...
متن کاملChoosability, Edge Choosability, and Total Choosability of Outerplane Graphs
Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...
متن کاملIncidence Choosability of Graphs
An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f) of G are adjacent whenever (i) v = w, or (ii) e = f , or (iii) vw = e or f . An incidence p-colouring of G is a mapping from the set of incidences of G to the set of colours {1, . . . , p} such that every two adjacent incidences receive distinct colours. In...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.05.017