Proportional choosability: A new list analogue of equitable coloring
نویسندگان
چکیده
منابع مشابه
A list analogue of equitable coloring
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 tha...
متن کاملEquitable List Coloring of Graphs
A graph G is equitably k-choosable if, for any k-uniform list assignment L, G admits a proper coloring π such that π(v) ∈ L(v) for all v ∈ V (G) and each color appears on at most |G|/k vertices. It was conjectured in [8] that every graph G with maximum degree ∆ is equitably k-choosable whenever k ≥ ∆ + 1. We prove the conjecture for the following cases: (i) ∆ ≤ 3; (ii) k ≥ (∆ − 1). Moreover, eq...
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A graph G is equitably k-choosable if for any k-uniform list assignment L, G is L-colorable and each color appears on at most d|V (G)|/ke vertices. A graph G is equitable kcolorable if G has a proper vertex coloring with k colors such that the size of the color classes differ by at most 1. In this paper, we prove that if G is a planar graph without 5and 7-cycles, then G is equitably k-choosable...
متن کاملEquitable List Coloring of Graphs with Bounded Degree
A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring of G such that every color class has at most d|G|/ke vertices. We prove results towards the conjecture that every graph with maximum degree at most r is equitably (r+1)choosable. In particular, we con rm the conjecture for r ≤ 7 and show that every graph with maximum degree at most r and at least r ve...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.05.011