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Ore conditions for antistrong digraphs

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  • Yuan, Lili
  • Meng, Jixiang

Abstract

In a digraph, an antidirected trail is a special trail satisfying that the arcs in the trail alternate between backward and forward arcs. For an antidirected trail, if it begins and ends with a forward arc, then it is a forward antidirected trail. A digraph D is said to be antistrong if there exist a forward antidirected (x,y)-trail for any x,y∈V(D). Suppose D is a non-bipartite digraph with |V(D)|≥3. Denote σ2(D)=min{d−(x)+d−(y),d+(x)+d+(y)|x,y∈V(D),xy∉A(D)}. This paper shows that D is antistrong if σ2(D)≥n for odd n or δ(D)≥2 and σ2(D)≥n−1 for even n. Furthermore, we give examples to demonstrate that all the results are best possible.

Suggested Citation

  • Yuan, Lili & Meng, Jixiang, 2023. "Ore conditions for antistrong digraphs," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003508
    DOI: 10.1016/j.amc.2023.128181
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