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- W2736760873 abstract "Abstract Let G be a 2-connected graph of order n, r a real number and Vr=v ϵ V(G)¦d(v)⩾r. It is shown that G contains a cycle missing at most max {0, n − 2r} vertices of Vr, yielding a common generalization of a result of Dirac and one of Shi Ronghua. A stronger conclusion holds if r⩾ 1 3 (n+2): G contains a cycle C such that either V(C)⊇Vr or ¦ V(C)¦⩾2r. This theorem extends a result of Haggkvist and Jackson and is proved by first showing that if r⩾ 1 3 (n+2), then G contains a cycle C for which ¦Vr∩V(C)¦is maximal such that N(x)⊆V(C) whenever x ϵ Vr − V(C) (∗). A result closely related to (∗) is stated and a result of Nash-Williams is extended using (∗)." @default.
- W2736760873 created "2017-07-31" @default.
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- W2736760873 date "1990-01-01" @default.
- W2736760873 modified "2023-09-26" @default.
- W2736760873 title "Cycles containing many vertices of large degree" @default.
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