A tight bound on the collection of edges in MSTs of induced subgraphs

Details A tight bound on the collection of edges in MSTs of induced subgraphs A tight bound on the collection of edges in MSTs of induced subgraphs

2007-05-16

arxiv.org/abs/0705.2439v1

Mathematics

Combinatorics

Scientific paper

Let $G=(V,E)$ be a complete $n$-vertex graph with distinct positive edge weights. We prove that for $k\in\{1,2,...,n-1\}$, the set consisting of the edges of all minimum spanning trees (MSTs) over induced subgraphs of $G$ with $n-k+1$ vertices has at most $nk-\binom{k+1}{2}$ elements. This proves a conjecture of Goemans and Vondrak \cite{GV2005}. We also show that the result is a generalization of Mader's Theorem, which bounds the number of edges in any edge-minimal $k$-connected graph.

Affiliated with

Also associated with

No associations

Rating

A tight bound on the collection of edges in MSTs of induced subgraphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A tight bound on the collection of edges in MSTs of induced subgraphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A tight bound on the collection of edges in MSTs of induced subgraphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-141804