标题： 最大化交替路径通过熵 显示英文标题

标题： Maximizing Alternating Paths via Entropy

摘要： 我们证明了如果$G$是一个$n$顶点图，其边被涂成红色和蓝色，那么长度为$2k+1$且包含$k+1$条红边和$k$条蓝边的颜色交替行走的数量最多为$k^k(k+1)^{k+1}(2k+1)^{-2k-1}n^{2k+2}$。这个问题是由 Basit, Granet, Horsley, Kündgen 和 Staden 最近提出的。 我们的证明涉及熵方法的应用。 显示英文摘要

摘要： We prove that if $G$ is an $n$-vertex graph whose edges are coloured with red and blue, then the number of colour-alternating walks of length $2k+1$ with $k+1$ red edges and $k$ blue edges is at most $k^k(k+1)^{k+1}(2k+1)^{-2k-1}n^{2k+2}$. This solves a problem that was recently posed by Basit, Granet, Horsley, K\"undgen and Staden. Our proof involves an application of the entropy method.