Cycles through a prescribed vertex set in N-connected graphs

Authors:
Ken-ichi Kawarabayashi
Affiliations:
Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

Citing 4
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Abstract

A well-known result of Dirac (Math. Nachr. 22 (1960) 61) says that given n vertices in an n- connected G, G has a cycle through all of them. In this paper, we generalize Dirac's result as follows: Given at most 3/2n vertices in an n-connected graph G when n ≥ 3 and |V(G)| ≥ 3/2 n, then G has a cycle through exactly n vertices of them.This improves the previous known bound given by Kaneko and Saito (J. Graph Theory 15(6)0 (1991) 655).