论文标题
锦标赛甚至图表都是平等的
Tournaments and Even Graphs are Equinumerous
论文作者
论文摘要
如果其边缘的方向和自动形态逆转其边缘的奇数，甚至是其他情况，则称为奇数。 PontusvonBrömssen（NéAndersson）表明，这种自动形态的存在与方向无关，并考虑了计数成对的非同构甚至图的问题。根据计算证据，他提出了一个相当令人惊讶的猜想，即$ n $顶点上的成对非晶状体数量甚至相当于$ n $顶点上的成对非同构比赛的数量。我们使用计数参数证明了这一猜想，该参数与Cauchy-Frobenius定理的多个应用程序。
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von Brömssen (né Andersson) showed that the existence of such an automorphism is independent of the orientation, and considered the question of counting pairwise non-isomorphic even graphs. Based on computational evidence, he made the rather surprising conjecture that the number of pairwise non-isomorphic even graphs on $n$ vertices is equal to the number of pairwise non-isomorphic tournaments on $n$ vertices. We prove this conjecture using a counting argument with several applications of the Cauchy-Frobenius Theorem.
