论文标题
关于颜色同构细分
On color isomorphic subdivisions
论文作者
论文摘要
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 $H$.在本文中，我们证明了$ f_ {2}（n，h_ {t}）=ω（n^{1+ \ frac {1} {2t-3}}）$，其中$ h_ {t} $是$ 1 $ -1 $ -subdivision $ 1 $ -subdivision $ k_ {t} $。这回答了Conlon和Tyomkyn的问题（Arxiv：2002.00921）。
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 $H$. In this paper, we prove that $f_{2}(n,H_{t})=Ω(n^{1+\frac{1}{2t-3}})$ where $H_{t}$ is the $1$-subdivision of the complete graph $K_{t}$. This answers a question of Conlon and Tyomkyn (arXiv: 2002.00921).
