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arXiv · 2002.01266

Packing a number of copies of a $(p,\,q)$-graph

Yun Wang·Jin Yan
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Abstract

Let $k,p,q$ be three positive integers. A graph $G$ with order $n$ is said to be $k$-placeable if there are $k$ edge disjoint copies of $G$ in the complete graph on $n$ vertices. A $(p,\,q)$-graph is a graph of order $p$ with $q$ edges. Packing results have proved useful in the study of the complexity of graph properties. Bollob\'{a}s et al. investigated the $k$-placeable of $(n,\,n-2)$-graphs and $(n,\,n-1)$-graphs with $k=2$ and $k=3$. Motivated by their results, this paper characterizes $(n,\,n-1)$-graphs with girth at least $9$ which are $4$-placeable. We also consider the $k$-placeable of $(n,\,n+1)$-graphs and 2-factors.

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Yun Wang, Jin Yan. 2020-02-04. Packing a number of copies of a $(p,\,q)$-graph. https://arxiv.org/abs/2002.01266

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