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Anti-Eulerian digraphs
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DOI：10.1016/j.amc.2021.126513.png)
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摘要
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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 is an element of V (T). The Cartesian product of two directed cycles (C-n1) over right arrow square (C-n2) over right arrow is anti-Eulerian if and only if gcd(n(1), n(2)) = 1. If n(1), n(2), ..., n(2k) can be partitioned into k relatively prime pairs, then (C-n1) over right arrow square (C-n2) over right arrow square ... square(C-n2k) over right arrow is anti-Eulerian. If each of D-i (1 <= i <= k) is an anti-Eulerian digraph and at least one of them is not a bipartite digraph, then D-1 square D-2 square ... square D-k is anti-Eulerian. (C) 2021 Elsevier Inc. All rights reserved.
Keyword:
Anti-directed cycle
Euler trail
Cartesian product
Tournament
Digraph
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