Some new results on repeated patterns in proper edge colorings

题目：Some new results on repeated patterns in proper edge colorings

报告人：张韬（之江实验室）

时间、地点：2023年6月28日8：30-10：30，海纳楼2幢203

摘要：In this talk, we will study a new extremal problem recently posed by Conlon and Tyomkyn [Repeated patterns in proper colourings, SIDMA, 2021]. Given a graph $H$ and an integer $k\geqslant 2$, let $f_{k}(n,H)$ be the smallest number of colors $c$ such that there exists a proper edge-coloring of the complete graph $K_{n}$ with $c$ colors containing no $k$ vertex-disjoint color-isomorphic copies of $H$. Using algebraic properties of polynomials over finite fields, we give an explicit edge-coloring of $K_{n}$ and show that $f_{k}(n, C_{4})=\Theta(n)$ when $k\ge 3$.