论文标题
实现图中的集团
Cliques in realization graphs
论文作者
论文摘要
实现图$ \ MATHCAL {g}（d）度序列$ d $的$是其顶点的图形，其标记为$ d $的实现，其中边缘通过交换单个边缘而与之相差。 Barrus [在度量序列的实现图上，离散数学，第1卷。 339（2016），没有。 8，pp。2146-2152]表征了$ \ mathcal {g}（d）$的$ d $是无三角形的。在这里，对于任何$ n \ geq 4 $，我们描述了一个实现$ d $的结构，该结构确切地决定了$ g（d）$的大小$ n $。结果，我们确定$ \ Mathcal {g}（d）$的度序列$ d $是$ n $顶点上的完整图。
The realization graph $\mathcal{G}(d)$ of a degree sequence $d$ is the graph whose vertices are labeled realizations of $d$, where edges join realizations that differ by swapping a single pair of edges. Barrus [On realization graphs of degree sequences, Discrete Mathematics, vol. 339 (2016), no. 8, pp. 2146-2152] characterized $d$ for which $\mathcal{G}(d)$ is triangle-free. Here, for any $n \geq 4$, we describe a structure in realizations of $d$ that exactly determines whether $G(d)$ has a clique of size $n$. As a consequence we determine the degree sequences $d$ for which $\mathcal{G}(d)$ is a complete graph on $n$ vertices.
