论文标题
单色组件有多个边缘
Monochromatic components with many edges
论文作者
论文摘要
给定完整图$ k_n $的$ r $ edged颜色，单色连接组件中最大的边缘数量是多少？这个自然的问题直到最近才受到应有的关注，当$ r = 2 $或$ 3 $时，作者的两个不相交子集的工作解决了。在这里，我们介绍了一个通用框架，用于研究此问题并将其应用于完全解决$ r = 4 $的情况，表明任何$ 4 $ edge-the $ k_n $的颜色包含具有至少$ \ frac {1} {1} {1} {12} {12} {12} \ binom {n} $ edge的单色组件，而$ eft $ ext $ ns $ \ frac}与Gyárfás的一定构造相匹配。
Given an $r$-edge-coloring of the complete graph $K_n$, what is the largest number of edges in a monochromatic connected component? This natural question has only recently received the attention it deserves, with work by two disjoint subsets of the authors resolving it for the first two special cases, when $r = 2$ or $3$. Here we introduce a general framework for studying this problem and apply it to fully resolve the $r = 4$ case, showing that any $4$-edge-coloring of $K_n$ contains a monochromatic component with at least $\frac{1}{12}\binom{n}{2}$ edges, where the constant $\frac{1}{12}$ is optimal only when the coloring matches a certain construction of Gyárfás.
