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doi:10.1016/j.dam.2004.06.010 
Copyright © 2004 Elsevier B.V. All rights reserved.
Connected triangle-free m-step competition graphs
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Geir T. Helleloid
Received 17 September 2001;
revised 8 April 2003;
accepted 4 June 2004.
Available online 4 August 2004.
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.
Keywords: Competition graph; m-step competition graph; m-step competition number
Article Outline
- 1. Introduction
- 2. When Pn is an m-step competition graph
- 3. Preliminaries on connected triangle-free graphs
- 4. The theorem on connected triangle-free graphs
- 5. An inequality for m-step competition numbers
- 6. Conclusion
- Acknowledgements
- References
