Reinforcing a Matroid to Have k Disjoint Bases

DOI: 10.4236/am.2010.13030   PDF   HTML     4,320 Downloads   7,637 Views   Citations


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].

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H. Lai, P. Li, Y. Liang and J. Xu, "Reinforcing a Matroid to Have k Disjoint Bases," Applied Mathematics, Vol. 1 No. 3, 2010, pp. 244-249. doi: 10.4236/am.2010.13030.

Conflicts of Interest

The authors declare no conflicts of interest.


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