EQUITABLE COLORING OF SPARSE PLANAR GRAPHS

作者:Luo Rong*; Sereni Jean Sebastien; Stephens D Christopher; Yu Gexin
来源:SIAM Journal on Discrete Mathematics, 2010, 24(4): 1572-1583.
DOI:10.1137/090751803

摘要

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 chi(eq)*(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, chi(eq)*(G) <= 4 if the girth of G is at least 10, and chi(eq)*(G) <= 3 if the girth of G is at least 14.

  • 出版日期2010