2020/02/17 by Tao Zhang, Zixiang Xu, Zhang, Tao +3
Computer Science · Mathematics · #05C35 #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05C35
paper · pdf · doi:10.48550/arxiv.2002.06795
15 pages
arxiv created 2020/02/17 · openalex publication_date 2020/02/17 · arxiv updated 2020/02/18 · openalex created_date 2020/02/24 · openalex updated_date 2026/07/28
For a graph H, the 1-subdivision of H, denoted by H', is the graph obtained by replacing the edges of H by internally disjoint paths of length 2. Recently, Conlon, Janzer and Lee (arXiv: 1903.10631) asked the following question: For any integer s≥2, estimate the smallest t such that \textupex(n,Ks,t')=Ω(n(3)/(2)-(1)/(2s)). In this paper, we consider the case s=3. More precisely, we provide an explicit construction giving ex(n,K3,30')=Ω(n(4)/(3)), which reduces the estimation for the smallest value of t from a magnitude of 1056 to the number 30. The construction is algebraic, which is based on some equations over finite fields.