AN ALGORITHM FOR CONSTRUCTING A k-TREE FOR A k-CONNECTED MATROID

نویسنده

  • NICK BRETTELL
چکیده

For a k-connected matroid M , Clark and Whittle showed there is a tree that displays, up to a natural equivalence, all non-trivial k-separations of M . In this paper, we present an algorithm for constructing such a tree, and prove that, provided the rank of any subset of E(M) can be found in constant time, the algorithm runs in polynomial time in |E(M)|.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Constructing a 3-tree for a 3-connected Matroid

In an earlier paper with Whittle, we showed that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3connected matroid M . The purpose of this paper is to give a polynomial-time algorithm for constructing such a tree for M .

متن کامل

An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree

In this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. Let $T=(V,E)$ be a tree. The $(k,l)$-core of $T$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. We show that, when the sum of the weights of vertices is negative, t...

متن کامل

On Generation of Cut Conjunctions, Minimal K-connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices

OF THE DISSERTATION On Generation of Cut Conjunctions, Minimal k-Connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices by Konrad Borys Dissertation Director: Professor Endre Boros We consider the following problems: • Cut conjunctions in graphs: given an undirected graphG = (V,E) and a collection of vertex pairs B ⊆ V × V generate all minimal edge sets X ⊆ E such tha...

متن کامل

Reinforcing a Matroid to Have k Disjoint Bases

Let ( ) M  denote the maximum number of disjoint bases in a matroid M . For a connected graph G , let ( ) = ( ( )) G M G   , where ( ) M G is the cycle matroid of G . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs G with ( ) G k   . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid M with ( ) M k   , elements ( ) e E...

متن کامل

The structure of the 3-separations of 3-connected matroids

Tutte defined a k–separation of a matroid M to be a partition (A, B) of the ground set of M such that |A|, |B| ≥ k and r(A) + r(B) − r(M) < k. If, for all m < n, the matroid M has no m–separations, then M is n–connected. Earlier, Whitney showed that (A, B) is a 1–separation of M if and only if A is a union of 2–connected components of M . When M is 2–connected, Cunningham and Edmonds gave a tre...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014