IJPAM: Volume 92, No. 1 (2014)

EQUITABLE DEFECTIVE COLORINGS OF
COMPLETE BIPARTITE GRAPHS

Keaitsuda Nakprasit$^1$, Sukanda Cummuang$^2$
$^1$Department of Mathematics
Faculty of Science
Khon Kaen University
40002, THAILAND
$^2$Centre of Excellence in Mathematics
PERDO, Bangkok, 10400, THAILAND


Abstract. A graph $G$ has an equitable $k$-defective coloring in $m$ colors if its vertices can be colored with $m$ colors such that the maximum degree of any subgraph induced by vertices assigned to the same color is at most $k$ and the numbers of vertices in any two sets composed of the vertices that are assigned to the same color differ by at most one. The equitable $k$-defective chromatic number of a graph $G,$ denoted by $\chi_{ED, k} (G),$ is the smallest positive integer $m$ for which $G$ has an equitable $k$-defective coloring in $m$ colors. In this paper, we present the equitable $k$-defective chromatic numbers of complete bipartite graphs for $k=1$ and $k=2.$

Received: December 11, 2013

AMS Subject Classification: 05C15, 05C35

Key Words and Phrases: equitable defective coloring, complete bipartite graph

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DOI: 10.12732/ijpam.v92i1.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 1
Pages: 73 - 86

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).