A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V(G)|. We show that if G is 4-connected, claw-free, and P _(10)-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P _9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pairs of forbidden subgraphs, [J Graph Theory 47 (2004), 183-202].
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机译：如果G包含从3到| V（G）|的所有长度的循环，则称图G为全循环的。我们表明，如果G是4连通的，无爪的且无P _（10），则G要么是泛环的，要么是Petersen图的线图。这意味着每一个4个连接，无爪，无P _9的图都是泛环图，这是最佳可能，并且扩展了Gould等人的结果。 3连通图中的泛环性：禁止子图对，[J Graph Theory 47（2004），183-202]。
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