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- W2022057215 abstract "Let G be a graph of order n and S be a vertex set of q vertices. We call G,S-pancyclable, if for every integer i with 3≤i≤q there exists a cycle C in G such that |V(C)∩S|=i. For any two nonadjacent vertices u,v of S, we say that u,v are of distance two in S, denoted by dS(u,v)=2, if there is a path P in G connecting u and v such that |V(P)∩S|≤3. In this paper, we will prove that if G is 2-connected and for all pairs of vertices u,v of S with dS(u,v)=2, max{d(u),d(v)}≥n2, then there is a cycle in G containing all the vertices of S. Furthermore, if for all pairs of vertices u,v of S with dS(u,v)=2, max{d(u),d(v)}≥n+12, then G is S-pancyclable unless the subgraph induced by S is in a class of special graphs. This generalizes a result of Fan [G. Fan, New sufficient conditions for cycles in graphs, J. Combin. Theory B 37 (1984) 221–227] for the case when S=V(G)." @default.
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- W2022057215 date "2009-01-01" @default.
- W2022057215 modified "2023-10-03" @default.
- W2022057215 title "A sufficient condition for pancyclability of graphs" @default.
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- W2022057215 doi "https://doi.org/10.1016/j.disc.2007.12.063" @default.
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