Discussiones Mathematicae Graph Theory 29(1) (2009) 119-142
doi: 10.7151/dmgt.1436

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EQUITABLE COLORING OF KNESER GRAPHS

Robert Fidytek, Hanna Furmańczyk, Paweł Żyliński

University of Gdańsk
Institute of Computer Science
80-952 Gdańsk, Poland

e-mail: {fidytek,hanna,pz}@inf.univ.gda.pl

Abstract

The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,…,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k) are discussed.

Keywords: equitable coloring, Kneser graph.

2000 Mathematics Subject Classification: 05C15, 05A18.

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Received 7 December 2007
Revised 9 May 2008
Accepted 9 May 2008