The competition number of a generalized line graph is at most two
Combinatorics
2012-08-10 v2
Abstract
In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this note, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.
Keywords
Cite
@article{arxiv.1110.2911,
title = {The competition number of a generalized line graph is at most two},
author = {Boram Park and Yoshio Sano},
journal= {arXiv preprint arXiv:1110.2911},
year = {2012}
}
Comments
13 pages, 4 figures