منابع مشابه
Equitable 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...
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...
متن کاملEquitable coloring of random graphs
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exists an equitable coloring of a graph G with k colors is said to be the equitable chromatic number of G and is denoted by χ=(G). The least positive integer k such that for any k′ ≥ k there exists an equitable coloring of ...
متن کاملA 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 کاملList-coloring embedded graphs
For any fixed surface Σ of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Σ is colorable from an assignment of lists of size three in time O(|V (G)|). Furthermore, we can allow a subgraph (of any size) with at most s components to be precolored, at the expense of increasing the time complexity of the algorithm to
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2004
ISSN: 1027-5487
DOI: 10.11650/twjm/1500407716