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Bootstrap Percolation, the Schröder Numbers, and the N -Kings Problem

✍ Scribed by Shapiro, Louis; Stephens, A. B.

Book ID
118199381
Publisher
Society for Industrial and Applied Mathematics
Year
1991
Tongue
English
Weight
525 KB
Volume
4
Category
Article
ISSN
0895-4801

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## Abstract For each __n__ and __k__, we examine bounds on the largest number __m__ so that for any __k__‐coloring of the edges of __K~n~__ there exists a copy of __K~m~__ whose edges receive at most __k−__1 colors. We show that for $k \ge \sqrt{n}\;+\,\Omega(n^{1/3})$, the largest value of __m__ i