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arXiv · 2006.06107

A note on the Tur\'an number of disjoint union of wheels

Chuanqi Xiao·Oscar Zamora
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Abstract

The Tur\'an number of a graph $H$, $\text{ex}(n,H)$, is the maximum number of edges in a graph on $n$ vertices which does not have $H$ as a subgraph. A wheel $W_n$ is an $n$-vertex graph formed by connecting a single vertex to all vertices of a cycle $C_{n-1}$. Let $mW_{2k+1}$ denote the $m$ vertex-disjoint copies of $W_{2k+1}$. For sufficiently large $n$, we determine the Tur\'an number and all extremal graphs for $mW_{2k+1}$. We also provide the Tur\'an number and all extremal graphs for $W^{h}:=\bigcup\limits^m_{i=1}W_{k_i}$ when $n$ is sufficiently large, where the number of even wheels is $h$ and $h>0$.

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Chuanqi Xiao, Oscar Zamora. 2020-06-10. A note on the Tur\'an number of disjoint union of wheels. https://arxiv.org/abs/2006.06107

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