A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs

摘要

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.