Geodesic
A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 173-184

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Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f_1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), d_K(u, v) = 2 implies min{ d_G(u), d_G(v) }≥n+1/2. In this paper we prove that every 2-connected { K_1,3 , P_5-f_1-heavy graph is pancyclic. This result completes the answer to the problem of finding f_1-heavy pairs of subgraphs implying pancyclicity of 2-connected graphs.
Keywords: cycle, Fan-type heavy subgraph, Hamilton cycle, pancyclicity 
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     title = {A {Fan-Type} {Heavy} {Pair} {Of} {Subgraphs} {For} {Pancyclicity} {Of} {2-Connected} {Graphs}},
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Wideł, Wojciech. A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 173-184. http://geodesic.mathdoc.fr/item/DMGT_2016_36_1_a12/