2025/03/07 by Zhao, Xiamiao, Yang, Yuxuan
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.05506
A graph G of order n is called edge-pancyclic if, for every integer k with 3 ≤ k ≤ n, every edge of G lies in a cycle of length k. Determining the minimum size f(n) of a simple edge-pancyclic graph with n vertices seems difficult. Recently, Li, Liu and Zhan \citeli2024minimum gave both a lower bound and an upper bound of f(n). In this paper, we improve their lower bound by considering a new class of graphs and improve the upper bound by constructing a family of edge-pancyclic graphs.