Spectral extremal graphs for intersecting cliques

By Dheer Noal Desai, Liying Kang, Yongtao Li, Zhenyu Ni, Michael Tait, Jing Wang. Linear Algebra and its Applications, 2021

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The (k, r)-fan is the graph consisting of k copies of the complete graph Kr which intersect in a single vertex, and is denoted by Fk,r . Erdős, Füredi, Gould and Gunderson [J. Combin. Theory Ser. B 64 (1995) 89–100] determined the maximum number of edges in an n-vertex graph that does not contain Fk,3 as a subgraph. Furthermore, Chen, Gould, Pfender and Wei [J. Combin. Theory Ser. B 89 (2003) 159–171] proved the analogous result on Fk,r for the general case r ≥ 3. In this paper, we show that for sufficiently large n, the graphs of order n that contain no copy of Fk,r and attain the maximum spectral radius are also edge-extremal. That is, such graphs must have ex(n, Fk,r) edges.

Subfields: Cellular and Molecular Neuroscience, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e35fff19398b053457c0bca770bccb78d099d300

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In Discrete Mathematics and Combinatorics

  1. Weijun Liu
  2. Yongtao Li
  3. Lihua Feng

In Geometry and Topology

  1. Weijun Liu
  2. Yongtao Li
  3. Lihua Feng

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