A note on the minimum size of a vertex pancyclic graph Original Research Article

Let G be a graph on n ⩾ 3 vertices. Then G is vertex pancyclic if every vertex of G is contained in cycles of length 3, 4, … , n. Let mn denote the minimum number of edges of a vertex pancyclic graph on n vertices. We show that m3 = 3, m4 = 5, m5 = 7, m6 = 9, and 32 n < mn ⩽ ⌈53n⌉ (n ⩾ 7).