Vertex pancyclicity in quasi claw-free graphs

This paper generalizes the concept of locally connected graphs. A graph G is triangularly connected if for every pair of edges image, G has a sequence of 3-cycles image such that image and image for image. In this paper, we show that every triangularly connected quasi claw-free graph on at least three vertices is vertex pancyclic. Therefore, the conjecture proposed by Ainouche is solved.