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The Edge-Integrity of Cartesian Products

The edge-integrity of a graph measures the difficulty of breaking it into pieces through the removal of a set of edges, taking into account both the number of edges removed and the size of the largest surviving component. We develop some techniques for bounding, estimating, and computing the edgeintegrity of products of graphs, paying particular attention to grid graphs. Correspondence to: Wayne Goddard Dept of Mathematics University of Pennsylvania Philadelphia PA 19103 wgoddard@math.upenn.edu