2-Factors with a Few Components in Balanced Bipartite Graphs

Abstract

In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2 n ( n ≥ 6 ) and e ( G ) > n 2 − 2 n + 4 contains a 2-factor with k components, 2 d 1 -cycle, ⋯ , 2 d k -cycle, if one of the following is satisfied: (1) k = 2 , δ ( G ) ≥ 2 and d 1 − 2 ≥ d 2 ≥ 2 ; (2) k = 3 , δ ( G ) ≥ d 3 + 2 and d 1 − 2 ≥ d 2 ≥ d 3 ≥ 4 . In particular, this extends one result of Moon and Moser in 1963 under condition (1).