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Cycles through specified vertices. (English) Zbl 0780.05033

The authors relax a minimum degree condition on a graph which guarantees long cycles and consider a set \(W\) of vertices with degree at least \(d\geq 1\), in a graph \(G\) with \(n\) vertices in total. Without imposing any further conditions on \(G\), it is shown that there is a cycle in \(G\) containing at least \(\bigl\lceil{| W|\over\lceil n/d\rceil- 1}\bigr\rceil\) vertices in \(W\). Extremal graphs are produced to show that the result is best possible.

MSC:

05C38 Paths and cycles
05C35 Extremal problems in graph theory
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References:

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