A list analogue of equitable coloring

Abstract

Given lists of available colors assigned to the vertices of a graph G, a list coloring is a proper coloring of G such that the color on each vertex is chosen from its list. If the lists all have size k, then a list coloring is equitable if each color appears on at most dn(G )/ke vertices. A graph is equitably k-choosable if such a coloring exists whenever the lists all have size k. We prove that G is equitably k-choosable when k ! maxfÁ(G ),n(G )/ ------------------ Kostochka and West

Extremal graph packing problems: Ore-type versus Dirac-type

“…A list analogue of equitable coloring was introduced by Kostochka, Pelsmajer and West [53]. A list assignment L for a graph G assigns to each vertex v ∈ V (G) a set L(v) of allowable colors.…”

“…Nevertheless, Kostochka, Pelsmajer and West [53] suggested that the following analogue of the Hajnal-Szemerédi Theorem holds.…”

On Equitable Coloring of d-Degenerate Graphs

“…In [17], a list analogue of equitable coloring was considered. A list assignment L for a graph G assigns to each vertex v ∈ V (G) a set L(v) of allowable colors.…”

Equitable coloring of random graphs

“…Lih's paper [14] surveys some basic results on equitable colorings and how the bound of ∆ + 1 can be replaced by ∆ for certain classes of graphs. Applications of the Hajnal-Szemerédi theorem and recent results on equitable colorings of graphs can be found in (among others) [1], [2], [9], [11], [12], [19]. Equitable coloring turned out to be useful in establishing bounds on tails of sums of dependent variables [6], [8], [18].…”