Connected triangle-free \(m\)-step competition graphs

DOI10.1016/j.dam.2004.06.010zbMath1066.05120OpenAlexW2033092574MaRDI QIDQ1765515

Geir T. Helleloid

Publication date: 23 February 2005

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2004.06.010

zbMATH Keywords

\(m\)-step competition numberCompetition graph

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75)

Related Items (14)

The \((1, 2)\)-step competition graph of a pure local tournament that is not round decomposable ⋮ The (1,2)-step competition graph of a tournament ⋮ On the limit of the sequence \(\{ C^m ( D ) \}_{m = 1}^\infty\) for a multipartite tournament \(D\) ⋮ On \(m\)-step competition graphs of bipartite tournaments ⋮ Digraphs whose \(m\)-step competition graphs are trees ⋮ A matrix sequence \(\{\Gamma (A^m)\}^\infty_{m=1}\) might converge even if the matrix \(A\) is not primitive ⋮ Competition periods of multipartite tournaments ⋮ A complete characterization of paths that are \(m\)-step competition graphs ⋮ On the matrix sequence \(\{\Gamma(A^m)\}_{m=1}^\infty\) for a Boolean matrix \(A\) whose digraph is linearly connected ⋮ Characterizing paths as \(m\)-step competition graphs ⋮ The competition number of a graph whose holes do not overlap much ⋮ The (1, 2)-step competition graph of a hypertournament ⋮ Note on the \(m\)-step competition numbers of paths and cycles ⋮ The \(m\)-step, same-step, and any-step competition graphs

Cites Work

• Two-step graphs of trees
• The \(m\)-step competition graph of a digraph
• Chromatic numbers of competition graphs
• Characterization of n-path graphs and of graphs having \(n\)-th root
• The \(m\)-step, same-step, and any-step competition graphs
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