论文标题
图形对称性参数与应用到诱导性的稳定性
Stability from graph symmetrisation arguments with applications to inducibility
论文作者
论文摘要
我们提出了可以通过Zykov的对称性来解决极端图问题的稳定性特性的足够条件。我们的标准根据问题的分析限制版本表示。 We show that, for example, it applies to the inducibility problem for an arbitrary complete bipartite graph $B$, which asks for the maximum number of induced copies of $B$ in an $n$-vertex graph, and to the inducibility problem for $K_{2,1,1,1}$ and $K_{3,1,1}$, the only complete partite graphs on at most five vertices for which the problem was previously open.
We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example, it applies to the inducibility problem for an arbitrary complete bipartite graph $B$, which asks for the maximum number of induced copies of $B$ in an $n$-vertex graph, and to the inducibility problem for $K_{2,1,1,1}$ and $K_{3,1,1}$, the only complete partite graphs on at most five vertices for which the problem was previously open.
