On the Three-matchings' Conjecture of Cubic Graphs (II)
Xiaoxin Song · Shuxue jikan · 2002
In 1994, FAN and RASPAUD posed the following conjecture: every bridgeless cubic graph contains three perfect matchings M 1, M 2 and M 3 such that M 1∩M 2∩M 3=*I.In this paper we obtain the following result: let G be a cyclely-4-edge-connected cubic graph, which has a perfect matching M 1 such that G-M 1 consists of four odd cycles. Then G contains two perfect matchings M 2 and M 3 such that M 1∩M 2∩M 3=*I.