The lower bound for the number of 1-factors in generalized Petersen graphs

Document Type : Research Paper


1 Department of Mathematics‎, ‎East China Normal University‎, ‎Shanghai‎, ‎200241‎, ‎P.R‎. ‎China

2 ‎Shanghai Key Laboratory of PMMP‎, ‎Shanghai‎, ‎200241‎, ‎P.R‎. ‎China.

3 School of Mathematics‎, ‎Physics and Statistics‎, ‎Shanghai University of Engineering Science‎, ‎Shanghai‎, ‎201620‎, ‎P.R‎. ‎China.

4 Department of Mathematics‎, ‎East China Normal University‎, ‎Shanghai‎, ‎200241‎, ‎P.R‎. ‎China.


‎In this paper‎, ‎we investigate the number of 1-factors of a‎ ‎generalized Petersen graph $P(N,k)$ and get a lower bound for the‎ ‎number of 1-factors of $P(N,k)$ as $k$ is odd‎, ‎which shows that the‎ ‎number of 1-factors of $P(N,k)$ is exponential in this case and‎ ‎confirms a conjecture due to Lovász and Plummer (Ann‎. ‎New York Acad‎. ‎Sci‎. ‎576(2006)‎, ‎no‎. ‎1‎, ‎389-398).


Main Subjects

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