Exact minimum codegree thresholds for K₄^--covering and K₅^--covering

2020/02/02 by Lei Yu, Xinmin Hou, Yu, Lei +5
Computer Science · Engineering · Mathematics · #05C35 #05C65 #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2002.00353

openalex publication_date 2020/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two 3-graphs F and H, an F-covering of H is a collection of copies of F in H such that each vertex of H is contained in at least one copy of them. Let c₂(n,F) be the maximum integer t such that every 3-graph with minimum codegree greater than t has an F-covering. In this note, we answer an open problem of Falgas-Ravry and Zhao (SIAM J. Discrete Math., 2016) by determining the exact value of c₂(n, K₄^-) and c₂(n, K₅^-), where K_t^- is the complete 3-graph on t vertices with one edge removed.

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