2024/04/17 by Chengli Li, Li, Chengli, Yurui Tang +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2404.11268
openalex publication_date 2024/04/17 · openalex created_date 2024/04/19 · openalex updated_date 2026/07/28
Recently, Ma, Qian and Shi determined the maximum size of an n-vertex graph with given fractional matching number s and maximum degree at most d. Motivated by this result, we determine the maximum number of ℓ-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma's result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree.