منابع مشابه
Matroid $T$-Connectivity
We introduce a new generalization of the maximum matching problem to matroids; this problem includes Gallai’s T path Problem for graphs.
متن کاملOn Maintaining Matroid 3-connectivity Relative to a Fixed Basis
We show that for any 3-connected matroid M on a ground set of at least four elements such that M does not contain any 4-element fans, and any basis B of M , there exists a set K ⊆ E(M) of four distinct elements such that for all k ∈ K, si(M/k) is 3-connected whenever k ∈ B, and co(M\k) is 3connected whenever k ∈ E(M) − B. Moreover, we show that if no other elements of E(M)−K satisfy this proper...
متن کاملMatroid 4-Connectivity: A Deletion-Contraction Theorem
A 3-separation (A, B), in a matroid M, is called sequential if the elements of A can be ordered (a1 , ..., ak) such that, for i=3, ..., k, ([a1 , ..., a i], [ai+1 , ..., ak] _ B) is a 3-separation. A matroid M is sequentially 4-connected if M is 3-connected and, for every 3-separation (A, B) of M, either (A, B) or (B, A) is sequential. We prove that, if M is a sequentially 4-connected matroid t...
متن کاملMatroid 3-connectivity and branch width
We prove that, for each nonnegative integer k and each matroid N , if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element set X ⊆ E(M) such that one of M \X and M/X is 3-connected and contains N as a minor.
متن کاملMatroid and Tutte-connectivity in Infinite Graphs
We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity function. As an application we re-prove that, also for infinite graphs, Tutte-connectivity is invariant under taking dual graphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00179-2