论文标题
棒棒糖边缘爆炸的极端图
Extremal graphs for edge blow-up of lollipops
论文作者
论文摘要
给定图形$ h $和一个整数$ p $（$ p \ geq 2 $），$ h $的边缘爆炸$ h^{p+1} $是通过用订单$（p+1）$替换$ h $中的每个边缘获得的图表，在该集团的新顶点的位置都是不同的。 Erds和Moon首先研究了用于比赛边缘的Turán数字。最近，Yuan已取得了$ H^{p+1} $的极端图，元素已由Yuan取得。当$ p \ geq 3 $和当$ p \ geqχ（h） +1 $ $ p \ geq 3 $的边缘爆炸范围和所有两分图的边缘爆炸范围范围。 Lollipop $ c_ {k，\; \ ell} $是通过将路径$ p _ {\ ell+1} $附加到其一个顶点中的$ c_k $获得的图表。在本文中，我们考虑了$ c_ {k，\; \ ell}^{p+1} $的极端图。
Given a graph $H$ and an integer $p$ ($p\geq 2$), the edge blow-up $H^{p+1}$ of $H$ is the graph obtained from replacing each edge in $H$ by a clique of order $(p+1)$, where the new vertices of the cliques are all distinct. The Turán numbers for edge blow-up of matchings were first studied by Erdős and Moon. Very recently some substantial progress of the extremal graphs for $H^{p+1}$ of larger $p$ has been made by Yuan. The range of Turán numbers for edge blow-up of all bipartite graphs when $p\geq 3$ and the exact Turán numbers for edge blow-up of all non-bipartite graphs when $p\geq χ(H) +1$ has been determined by Yuan (2022), where $χ(H)$ is the chromatic number of $H$. A lollipop $C_{k,\;\ell}$ is the graph obtained from a cycle $C_k$ by appending a path $P_{\ell+1}$ to one of its vertices. In this paper, we consider the extremal graphs for $C_{k,\;\ell}^{p+1}$ of the rest cases $p=2$ and $p=3$.
