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

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.

13 pages, 4 figures

References in corpus (3)

• The competition numbers of ternary Hamming graphs
• The competition numbers of Hamming graphs with diameter at most three
• The competition numbers of regular polyhedra