Uniquely K_r-Saturated Graphs
Combinatorics
2012-03-07 v1 Discrete Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.1203.1084,
title = {Uniquely K_r-Saturated Graphs},
author = {Stephen G. Hartke and Derrick Stolee},
journal= {arXiv preprint arXiv:1203.1084},
year = {2012}
}
Comments
35 pages, 23 figures