Abstract
Assume that the edges of the complete graphKnare given independent uniform [0, 1] weights. We consider the expected minimum total weightμkofk⩽ 2 edge-disjoint spanning trees. Whenkis large we show thatμk≈k2. Most of the paper is concerned with the casek= 2. We show thatm2tends to an explicitly defined constant and thatμ2≈ 4.1704288. . . .
Highlights
This paper can be considered to be a contribution to the following general problem
The minimum spanning tree problem is a special case of the problem of finding a minimum weight basis in an element weighted matroid
Before proceeding to the proofs of Theorems 1 and 2 we note some properties of the κ-core of a random graph
Summary
We are given a combinatorial optimization problem where the weights of variables are random. What can be said about the random variable equal to the minimum objective value in this model. The minimum spanning tree problem is a special case of the problem of finding a minimum weight basis in an element weighted matroid. Extending the result of [10] has proved to be difficult for other matroids. Given a connected simple graph G = (V, E) with edge lengths x = (xe : e ∈ E) and a positive integer k, let mstk(G, x) denote the minimum length of k edge disjoint spanning trees of G. Before proceeding to the proofs of Theorems 1 and 2 we note some properties of the κ-core of a random graph
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
