# Potentially $K {m}-G$-graphical Sequences: A Survey - Mathematics > Combinatorics

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Abstract: The set of all non-increasing nonnegative integers sequence $\pi=$$dv 1,$ $dv 2,$ $

.,$ $dv n$ is denoted by $NS n$.A sequence $\pi\in NS n$ is said to be graphic if it is the degree sequenceof a simple graph $G$ on $n$ vertices, and such a graph $G$ is called arealization 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 arealization 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 graphobtained from $K {m}$ by removing the edges set $EH$ of the graph $H$ $H$ isa subgraph of $K {m}$. This paper summarizes briefly some recent results onpotentially $K {m}-G$-graphic sequences and give a useful classification fordetermining $\sigmaH,n$.

Author: ** Chunhui Lai, Lili Hu**

Source: https://arxiv.org/