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On d-arc-dominated Oriented Graphs


We consider only digraphs that are oriented graphs, meaning orientations of simple finite graphs. An oriented graph D = (V, A) with minimum outdegree d is called d-arc-dominated if for every arc \({(x, y) \in A}\) there is a vertex \({u \in V}\) with outdegree d such that both \({(u, x) \in A}\) and \({(u, y) \in A}\) hold. In this paper, we show that for any integer d ≥ 3 the girth of a d-arc-dominated oriented graph is less than or equal to d. Moreover, for every integer t with 3 ≤ t ≤ d there is a d-arc-dominated oriented graph with girth t. We also give a characterization for oriented graphs with both minimum outdegree and girth d to be d-arc-dominated and classify all d-arc-dominated d-circular oriented graphs with girth d.

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  1. Bang-Jensen J., Gutin G.: Digraphs: Theory, Algorithms and Applications. Springer, London (2001)

    Google Scholar 

  2. Bermond J.-C., Thomassen C.: Cycles in digraphs—a survey. J. Graph Theory 5, 1–43 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cameron P.J., West D.B.: Research problems from the 20th British combinatorial conference. Discrete Math. 308, 621–630 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Tan N.D.: 3-arc-dominated digraphs. SIAM J. Discrete Math. 24, 1153–1161 (2010)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Ngo Dac Tan.

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This research was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED), Project No

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Tan, N.D. On d-arc-dominated Oriented Graphs. Graphs and Combinatorics 30, 1045–1054 (2014).

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Mathematics Subject Classification (2000)