论文标题
车轮的极端图
Extremal graphs for wheels
论文作者
论文摘要
对于图$ h $，由ex $（n，h）$表示的$ h $的turán数字是$ n $ vertex $ h $ h $ free Graph的最大边数。令$ g（n，h）$表示任何单色副本中未包含的最大边数，$ h $ in $ 2 $ edge-edge-edge-edge-edge-edge-edge-edgromoring $ k_n $。车轮$ w_m $是将单个顶点连接到长度$ m-1 $的所有顶点而形成的图。 $ W_ {2K} $的Turán数在1960年代由Simonovits确定。在本文中，当$ n $足够大时，我们确定ex $（n，w_ {2k+1}）$。我们还表明，对于足够大的$ n $，$ g（n，w_，w_ {2k+1}）= \ mbox {ex}（ex}（n，w_ {2k+1}）$，确认了Keevash和Sudakov对Odd Wheels的猜想。
For a graph $H$, the Turán number of $H$, denoted by ex$(n,H)$, is the maximum number of edges of an $n$-vertex $H$-free graph. Let $g(n,H)$ denote the maximum number of edges not contained in any monochromatic copy of $H$ in a $2$-edge-coloring of $K_n$. A wheel $W_m$ is a graph formed by connecting a single vertex to all vertices of a cycle of length $m-1$. The Turán number of $W_{2k}$ was determined by Simonovits in the 1960s. In this paper, we determine ex$(n,W_{2k+1})$ when $n$ is sufficiently large. We also show that, for sufficiently large $n$, $g(n,W_{2k+1})=\mbox{ex}(n,W_{2k+1})$ which confirms a conjecture posed by Keevash and Sudakov for odd wheels.
