Anti-Eulerian digraphs

Bo Zhang and Baoyindureng Wu

Applied Mathematics and Computation, 2021, vol. 411, issue C

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.

Keywords: Anti-directed cycle; Euler trail; Cartesian product; Tournament; Digraph (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321006020
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006020

DOI: 10.1016/j.amc.2021.126513

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().