Connected triangle-free m-step competition graphs

  title={Connected triangle-free m-step competition graphs},
  author={Geir T. Helleloid},
  journal={Discrete Applied Mathematics},
In 1968, Cohen presented competition graphs in connection with the study of ecological systems. Recently, Cho, Kim and Nam introduced a generalization called the m-step competition graph. In this paper, we characterize connected triangle-free m-step competition graphs on n vertices form n. The analogous result follows for same-step competition graphs. We also demonstrate that the path on n vertices is an(n − 1)-step and an(n − 2)-step competition graph. Finally, we resolve a question of Cho… CONTINUE READING

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