Geodesic
A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 477-499

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A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ 3, . . ., n. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs ℋ we say that G is ℋ-f1-heavy, if G is H-f1-heavy for every graph H ∈ℋ. Let D denote the deer, a graph consisting of a triangle with two disjoint paths P3 adjoined to two of its vertices. In this paper we prove that every 2-connected K1,3, P7, D-f1-heavy graph on n ≥ 14 vertices is pancyclic. This result extends the previous work by Faudree, Ryjáček and Schiermeyer.
Keywords: cycle, Fan-type heavy subgraph, Hamilton cycle, pancyclicity 
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     author = {Wide, Wojciech},
     title = {A {Triple} of {Heavy} {Subgraphs} {Ensuring} {Pancyclicity} of {2-Connected} {Graphs}},
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Wide, Wojciech. A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 477-499. http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a11/