Author(s)

Hong-Jian Lai, Ping Li, Yanting Liang, Jinquan Xu

.

Let denote the maximum number of disjoint bases in a matroid . For a connected graph , let , where is the cycle matroid of . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid with , elements with the property that have been characterized in terms of matroid invariants such as strength and -partitions. In this paper, we consider matroids with , and determine the minimum of , where is a matroid that contains as a restriction with both and . This minimum is expressed as a function of certain invariants of , as well as a min-max formula. These are applied to imply former results of Haas [3] and of Liu et al. [4].

Disjoint Bases, Edge-Disjoint Spanning Trees, Spanning Tree Packing Numbers, Strength,

Lai, H. , Li, P. , Liang, Y. and Xu, J. (2010) Reinforcing a Matroid to Have k Disjoint Bases. Applied Mathematics, 1, 244-249. doi: 10.4236/am.2010.13030.