Abstract

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 for m ⩾ 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, Kim and Nam on an inequality between 1-step and m-step competition numbers.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.