Abstract
The paper is concerned with the longest cycles in regular three- (or two-) connected graphs. In particular, the following results are proved: (i) every 3-connected k-regular graph on n vertices has a cycle of length at least min(3 k, n); (ii) every 2-connected k-regular graph on n vertices, where n < 3 k + 4, has a cycle of length at least min(3 k, n).
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