简单图中顶点度的最大 spread
Maximum spread of vertex degrees in a simple graph
浏览论文内容
中文总结 AI 辅助
该研究针对无向简单图，定义度差小于$k$的无序顶点对数量$h_k(G)$，旨在确定其最小值$f(n,k)$，其二分图类似情形曾用于证明Burdzy–Pitman猜想。
中文摘要 AI 辅助
我们考虑如下问题：设$n>k$为正整数，$G$是具有$n$个顶点的图（无向、无环且无重边）。令$h_k(G)$表示图$G$中度差小于$k$的无序顶点对的数量。我们旨在确定$h_k(G)$的最小可能值$f(n,k)$。该问题的研究动机在于，此问题的二分图类似情形使S. Cichomski与F. Petrov[CP]得以证明关于独立同分布随机变量 spread 的Burdzy–Pitman猜想。
英文摘要
We consider the following problem: let $n>k$ --- positive integers, $G$ --- a graph on $n$ vertices (undirected, without loops or multiple edges). Let $h_k(G)$ denote the number of unordered pairs of vertices of the graph $G$ whose degrees differ by less than $k$. We seek to determine the smallest possible value $f(n,k)$ of $h_k(G)$. The interest in this question is motivated by the fact that the bipartite analogue of the problem allowed S. Cichomski and F. Petrov \cite{CP} to prove the Burdzy--Pitman conjecture on the spread of independent identically distributed random variables.
