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 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k compon...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 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k components, 2d1-cycle, ⋯, 2dk-cycle, if one of the following is satisfied: (1) k=2, δ(G)≥2and d1−2≥d2≥2;(2) k=3, δ(G)≥d3+2and d1−2≥d2≥d3≥4. In particular, this extends one result of Moon and Moser in 1963 under condition (1).展开更多
文摘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 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k components, 2d1-cycle, ⋯, 2dk-cycle, if one of the following is satisfied: (1) k=2, δ(G)≥2and d1−2≥d2≥2;(2) k=3, δ(G)≥d3+2and d1−2≥d2≥d3≥4. In particular, this extends one result of Moon and Moser in 1963 under condition (1).
基金Supported by National Natural Science Foundation of China(No.11071002)Program for New Century Excellent Talents in University,Key Project of Chinese Ministry of Education(No.210091)+4 种基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20103401110002)Science and Technological Fund of Anhui Province for Outstanding Youth(No.10040606Y33)National Science Foundation of the Department of Education of Anhui Province(Nos.KJ2011A195,KJ2010B136)Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(No.KJJQ1001)Project for Academic Innovation Team of Anhui University(No.KJTD001B)
