Equitable coloring planar graphs with large girth
نویسندگان
چکیده
A proper vertex coloring of a graph G is equitable if the size of color classes differ by at most one. The equitable chromatic threshold of G, denoted by ∗Eq(G), is the smallest integer m such that G is equitably n-colorable for all n m. We prove that ∗Eq(G) = (G) if G is a non-bipartite planar graph with girth 26 and (G) 2 or G is a 2-connected outerplanar graph with girth 4. © 2007 Elsevier B.V. All rights reserved.
منابع مشابه
Equitable Coloring of Sparse Planar Graphs
A proper vertex coloring of a graph G is equitable if the sizes of color classes differ by at most one. The equitable chromatic threshold χeq(G) of G is the smallest integer m such that G is equitably n-colorable for all n ≥ m. We show that for planar graphs G with minimum degree at least two, χeq(G) ≤ 4 if the girth of G is at least 10, and χeq(G) ≤ 3 if the girth of G is at least 14.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008