Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2021-07-17 , DOI: 10.1016/j.amc.2021.126513 Bo Zhang 1 , Baoyindureng Wu 1
Let be a digraph. A closed anti-directed Euler trail of is a closed trail in which consecutive arcs have opposite directions and each arc of occurs exactly once. A digraph is anti-Eulerian if it contains a closed anti-directed Euler trail. A tournament is anti-Eulerian if and only if both and are even for any . The Cartesian product of two directed cycles is anti-Eulerian if and only if . If can be partitioned into relatively prime pairs, then is anti-Eulerian. If each of () is an anti-Eulerian digraph and at least one of them is not a bipartite digraph, then is anti-Eulerian.
中文翻译:
反欧拉有向图
让 是一个有向图。一个封闭的反方向欧拉轨迹 是一条封闭的轨迹,其中连续的弧具有相反的方向,每个弧的 恰好发生一次。如果一个有向图包含一个封闭的反定向欧拉轨迹,那么它就是反欧拉轨迹。一场比赛 是反欧拉的当且仅当两者 和 甚至对于任何 . 两个有向循环的笛卡尔积 是反欧拉当且仅当 . 如果 可以分为 相对质数对,那么 是反欧拉的。如果每个 () 是一个反欧拉有向图并且其中至少一个不是二部有向图,那么 是反欧拉的。