DOIAbstract
AbstractIn this paper, we consider the length of the longest cycle through specified vertices. We show the following three results. 1.(1) Let G be a k-connected graph of order at least 2k and circumference l. Suppose m<k. Then for any m vertices of G, G has a cycle which contains all of them and has length at least ((k − m)k)l + 2m.2.(2) Let G be a k-connected k-regular graph of order at least 2k and circumference l. For any k vertices of G, there exists a cycle which contains all of them and has length at least (13k)l + 23(k + 2).3.(3) Let G be a 3-connected planar graph with circumference l. Then for any three vertices of G, there exists a cycle which contains all of them and has length at least 14l + 3
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