The competition number of a generalized line graph is at most two

Details The competition number of a generalized line graph is at most two The competition number of a generalized line graph is at most two

2011-10-13

arxiv.org/abs/1110.2911v1

Mathematics

Combinatorics

12 pages, 3 figures

Scientific paper

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.

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