摘要
Let G be a circuit graph of a connected matroid. P. Li and G. Liu [Comput. Math. Appl., 2008, 55： 654-659] proved that G has a Hamilton cycle including e and another Hamilton cycle excluding e for any edge e of G if G has at least four vertices. This paper proves that G has a Hamilton cycle including e and excluding e＇ for any two edges e and e＇ of G if G has at least five vertices. This result is best possible in some sense. An open problem is proposed in the end of this paper.
Let G be a circuit graph of a connected matroid. P. Li and G. Liu [Comput. Math. Appl., 2008, 55： 654-659] proved that G has a Hamilton cycle including e and another Hamilton cycle excluding e for any edge e of G if G has at least four vertices. This paper proves that G has a Hamilton cycle including e and excluding e＇ for any two edges e and e＇ of G if G has at least five vertices. This result is best possible in some sense. An open problem is proposed in the end of this paper.
基金
The authors would like to thank the referees for providing some very helpful suggestions for revising this paper. This work was supported by the National Natural Science Foundation of China （Grant No. 61070230）.
