ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2019: 0.600
Rejection Rate (2018-2019): c. 84%
Mathematicae Graph Theory 20(2) (2000) 165-172 DOI: 10.7151/dmgt.1116
Georgia State University, Atlanta, GA 30303
Jill R. Faudree
University of Alaska Fairbanks, Fairbanks, AK 99775
Ronald J. Gould
Emory University, Atlanta, GA 30322
Nihon University, Tokyo 156, Japan
We consider the question of the range of the number of cycles possible in a 2-factor of
a 2-connected claw-free graph with sufficiently high minimum degree. (By claw-free we mean
the graph has no induced K1,3.) In particular, we show that for such a graph G
of order n ≥ 51 with δ(G) ≥ [(n−2)/3], G contains a 2-factor with
exactly k cycles, for 1 ≤ k ≤ [(n−24)/3]. We also show that this result is sharp in the sense that if
we lower δ(G), we cannot obtain the full range of values for k.
Keywords: claw-free, forbidden subgraphs, 2-factors, cycles.
2000 Mathematics Subject Classification: 05C38.
Received 19 February 1999
Revised 24 January 2000