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Many cliques with few edges and bounded maximum degree
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2021-06-08 , DOI: 10.1016/j.jctb.2021.05.005
Debsoumya Chakraborti , Da Qi Chen

Generalized Turán problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant of this problem where the number of edges is fixed instead of the number of vertices. In this paper, we determine the maximum number of cliques of a fixed order in a graph with fixed number of edges and bounded maximum degree, resolving a conjecture by Kirsch and Radcliffe. We also give a complete characterization of the extremal graphs.



中文翻译:

许多边缘很少且最大度有界的派系

在过去的几十年中,广义图兰问题一直是极值组合学研究的中心课题。最近,Chase 完全解决了这样一个问题,即最大化具有固定顶点数和有界最大度的图中的固定顺序团的数量。Kirsch 和 Radcliffe 提出了这个问题的一个自然变体,其中边的数量是固定的,而不是顶点的数量。在本文中,我们确定具有固定边数和有界最大度的图中固定阶数的最大团数,解决了 Kirsch 和 Radcliffe 的猜想。我们还给出了极值图的完整表征。

更新日期:2021-06-08
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