The hamiltonicity on the competition graphs of round digraphs

  • Xin-hong Zhang
  • Rui-juan Li
  • Xiao-ting An


Given a digraph D = (V, A), the competition graph G of D, denoted by C(D), has the same set of vertices as D and an edge between vertices x and y if and only if ND+(x)∩ND+(y) 6≠0. In this paper, we investigate the competition graphs of round digraphs and give a necessary and suffcient condition for these graphs to be hamiltonian.


round digraph competition graph connected component hamiltonian 

MR Subject Classification

05C20 05C45 05C75 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We express our sincere thanks to the referees for their valuable suggestions and detailed comments.


  1. [1]
    J Bang-Jensen, G Gutin. Digraphs: Theory, Algorithms and Applications, Spring Monogr Math, Spring-Verlag, London, 2001.zbMATHGoogle Scholar
  2. [2]
    J E Cohen. Interval graphs and food webs: a finding and a problem, Rand Corporation Document 17696-PR, Santa Monica, CA, 1968.Google Scholar
  3. [3]
    R D Dutton, R C Brigham. A characterization of competition graphs, Discrete Appl Math, 1983, 6: 315–317.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    K A S Factor, S K Merz. The (1,2)-step competition graph of a tournament, Discrete Appl Math, 2011, 159: 100–103.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    K F Fraughnaugh, J R Lundgren, S K Merz, J S Maybee, N.J. Pullman. Competition graphs of strongly connected and hamiltonian digraphs, SIAM J Discrete Math, 1995, 8: 179–185.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    D R Guichard. Competition graphs of Hamiltonian digraphs, SIAM J Discrete Math, 1998, 11: 128–134.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J Huang. Which digraphs are round?, Australas J Combin, 1999, 19: 203–208.MathSciNetzbMATHGoogle Scholar
  8. [8]
    S R Kim. Competition graphs and scientific laws for food webs and other systems, PhD Thesis, Rutgers University, 1988.Google Scholar
  9. [9]
    S R Kim, J Y Lee, B Park, Y Sano. The competition graphs of oriented complete bipartite graphs, Discrete Appl Math, 2016, 201: 182–190.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    X Zhang, R Li, S Li, G Xu. A note on the existence of edges in the (1, 2)-step competition graph of a round digraph, Australas J Combin, 2013, 57: 287–292.MathSciNetzbMATHGoogle Scholar
  11. [11]
    X Zhang, R Li. The (1,2)-step competition graph of a pure local tournament that is not round decomposable, Discrete Appl Math, 2016, 205: 180–190.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsTaiyuan University of Science and TechnologyTaiyuanChina
  2. 2.School of Mathematical SciencesShanxi UniversityTaiyuanChina

Personalised recommendations