Balanced k-Coloring of Polyominos

Toshihiko TAKAHASHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.3   pp.517-520
Publication Date: 1994/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)
Category: Algorithms, Data Structure and Computational Complexity
polyomino,  graph,  coloring,  balanced coloring,  

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A polyomino is a configuration composed of squares connected by sharing edges. A k-coloring of a polyomino is an assignment of k colors to the squares of the polyomino in such a way no two adjacent squares receive the same color. A k-coloring is called balanced if the difference of the number of squares in color i and that of squares in color j is at most one for any two colors i and j. In this paper, we show that any polyomino has balanced k-coloring for k3.