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Anti-Eulerian digraphs

Author

Listed:
  • Zhang, Bo
  • Wu, Baoyindureng

Abstract

Let D be a digraph. A closed anti-directed Euler trail of D is a closed trail in which consecutive arcs have opposite directions and each arc of D occurs exactly once. A digraph is anti-Eulerian if it contains a closed anti-directed Euler trail. A tournament T is anti-Eulerian if and only if both d+(v) and d−(v) are even for any v∈V(T). The Cartesian product of two directed cycles Cn1→□Cn2→ is anti-Eulerian if and only if gcd(n1,n2)=1. If n1,n2,…,n2k can be partitioned into k relatively prime pairs, then Cn1→□Cn2→□⋯□Cn2k→ is anti-Eulerian. If each of Di (1≤i≤k) is an anti-Eulerian digraph and at least one of them is not a bipartite digraph, then D1□D2□⋯□Dk is anti-Eulerian.

Suggested Citation

  • Zhang, Bo & Wu, Baoyindureng, 2021. "Anti-Eulerian digraphs," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006020
    DOI: 10.1016/j.amc.2021.126513
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