Anti-Eulerian digraphs

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：Anti-directed cycle,Euler trail,Cartesian product,Tournament,Digraph

论文评审过程：Received 23 March 2021, Revised 2 July 2021, Accepted 5 July 2021, Available online 17 July 2021, Version of Record 17 July 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126513