, Volume 51, Issue 2, pp 603-619
Date: 21 Oct 2012

On maximal resonance of polyomino graphs

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Abstract

A polyomino graph is a finite plane 2-connected bipartite graph every interior face of which is bounded by a regular square of side length one. Let k be a positive integer, a polyomino graph G is k-resonant if the deletion of any ik vertex-disjoint squares from G results in a graph either having perfect matchings or being empty. If graph G is k-resonant for any integer k ≥ 1, then it is called maximally resonant. All maximally resonant polyomino graphs are characterized in this work. As a result, the least integer k such that a k-resonant polyomino graph is maximally resonant is determined.

Supported by NNSF of China (Grant no. 11126326;10801091;11201404) and NSF of Guangdong Province (s20120100815).