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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
##### Keywords:
extremal graphs; long cycles
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##### References:
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