Cycles through specified vertices


Recently, various authors have obtained results about the existence of long cycles in graphs with a given minimum degree d. We extend these results to the case where only some of the vertices are known to have degree at least d, and we want to find a cycle through as many of these vertices as possible. If G is a graph on n vertices and W is a set of w vertices of degree at least d, we prove that there is a cycle through at least {Mathematical expression} vertices of W. We also find the extremal graphs for this property. © 1993 Akadémiai Kiadò.

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