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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 paper, 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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Boram Park, Yoshio Sano. The competition number of a generalized line graph is at most two. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.1--10. ⟨hal-00990584⟩

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