Potentially $K_{m}-G$-graphical Sequences: A Survey

Lai Chunhui Minnan Normal University Hu Lili Minnan Normal University

Combinatorics mathscidoc:1612.06004

Czechoslovak Mathematical Journal, 59, 1059-1075, 2009.12
The set of all non-increasing nonnegative integers sequence $\pi=$ ($d(v_1 ),$ $d(v_2 ),$ $...,$ $d(v_n )$) is denoted by $NS_n$. A sequence $\pi\in NS_n$ is said to be graphic if it is the degree sequence of a simple graph $G$ on $n$ vertices, and such a graph $G$ is called a realization of $\pi$. The set of all graphic sequences in $NS_n$ is denoted by $GS_n$. A graphical sequence $\pi$ is potentially $H$-graphical if there is a realization of $\pi$ containing $H$ as a subgraph, while $\pi$ is forcibly $H$-graphical if every realization of $\pi$ contains $H$ as a subgraph. Let $K_k$ denote a complete graph on $k$ vertices. Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). This paper summarizes briefly some recent results on potentially $K_{m}-G$-graphic sequences and give a useful classification for determining $\sigma(H,n)$.
graph; degree sequence; potentially $K_{m}-G$-graphic sequences
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@inproceedings{lai2009potentially,
  title={Potentially $K_{m}-G$-graphical Sequences: A Survey},
  author={Lai Chunhui, and Hu Lili},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161227090515985375695},
  booktitle={Czechoslovak Mathematical Journal},
  volume={59},
  pages={1059-1075},
  year={2009},
}
Lai Chunhui, and Hu Lili. Potentially $K_{m}-G$-graphical Sequences: A Survey. 2009. Vol. 59. In Czechoslovak Mathematical Journal. pp.1059-1075. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161227090515985375695.
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