Connected triangle-free m-step competition graphs

@article{Helleloid2005ConnectedTM,
  title={Connected triangle-free m-step competition graphs},
  author={Geir T. Helleloid},
  journal={Discrete Applied Mathematics},
  year={2005},
  volume={145},
  pages={376-383}
}
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

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 12 references

A sufficient condition for a tree belonging to T(2,2

  • H. H. Cho, S.-R. Kim, Y. Nam
  • n), Congr. Numer
  • 1997

Chromatic numbers of competition graphs

  • J. R. Lundgren, S. K. Merz, C. W. Rasmussen
  • Linear Algebra Appl
  • 1995
1 Excerpt

Quintas(Eds.), Quo Vadis, Graph Theory

  • S.-R. Kim
  • Annals of Discrete Mathematics,
  • 1993

A sufficient condition for a tree belonging to T ( 2 , 2 , n )

  • Y. Nam S.-R. Kim
  • Combinatorial Matrix Theory
  • 1991

Combinatorial Matrix Theory

  • R. Brualdi, H. Ryser
  • 1991
1 Excerpt

Food webs, competition graphs, competition-common enemy graphs, and niche graphs, F.S. Roberts(Ed.), Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, IMH

  • J. R. Lundgren
  • Volumes in Mathematics and its Application,
  • 1989

Competition graphs and scientific laws for food webs and other systems, Ph.D

  • S.-R. Kim
  • 1988

Food webs, competition graphs, and the boxicity of ecological phase space, in:Y.Alavi, D

  • F. S. Roberts
  • Lick (Eds.), Theory andApplication of Graphs,
  • 1978

Similar Papers

Loading similar papers…