Uniquely K_r-Saturated Graphs

Details Uniquely K_r-Saturated Graphs Uniquely K_r-Saturated Graphs

2012-03-06

arxiv.org/abs/1203.1084v1

Mathematics

Combinatorics

35 pages, 23 figures

Scientific paper

A graph G is uniquely K_r-saturated if it contains no clique with r vertices and if for all edges e in the complement, G + e has a unique clique with r vertices. Previously, few examples of uniquely K_r-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear programs. We find several new uniquely K_r-saturated graphs with 4 \leq r \leq 7, as well as two new infinite families based on Cayley graphs for Z_n with a small number of generators.

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