Extremal problems for star forests and cliques

2024/04/09 by Lu, Yongchun, Yongchun Lu, Liying Kang +1 · 1 citation
Mathematics · #05C35 #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2404.05942

openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a family of graphs F, the Turán number ex(n, F) denotes the maximum number of edges in any F-free graph on n vertices. Recently, Alon and Frankl studied of maximum number of edges in an n-vertex \K_k+1, M_s+1\-free graph, where K_k+1 is a complete graph on k+1 vertices and M_s+1 is a matching of s+1 edges. They determined the exact value of ex(n, \K_k+1,M_s+1\). In this paper, we extend the matching M_s+1 to star forest (s+1)S_l, and determine the exact value of ex(n, \K_k+1,(s+1)S_l\) for sufficiently large enough n. Furthermore, all the extremal graphs are obtained.

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