We show that the spanning tree degree enumerator polynomial of a connected graph G is real stable if and only distance-hereditary.

We present two short proofs for Diestel's criterion that a connected graph has normal spanning tree provided it contains no subdivision of countable clique in which every edge been replaced by uncountably many parallel edges.

Inspired by the seminal works of Khuller et al. (SIAM J. Comput. 25(2), 355–368 (1996)) and Chan (Discrete Geom. 32(2), 177–194 (2004)) we study bottleneck version Euclidean bounded-degree spanning tree problem. A is a whose largest edge-length minimum, degree-K minimum. Let $$\beta _K$$ be supremum ratio to tree, over all finite point sets in plane. It known that _5=1$$ , it easy verify _2\geq...

The degree-constrained minimum spanning tree (DCMST) is relevant in the design of networks. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. Primal methods have not been used extensively in the past, and their performance ...

We present a distributed protocol for maintaining a maximum flow spanning tree in a network, with a designated node as the root of the tree. This maximum flow spanning tree can be used to route the allocation of new virtual circuits whose destination is the designated node. As virtual circuits are allocated and removed, the available capacity of the channels in the network changes, causing the ...

A formulation of a graph problem for scheduling parallel computations of multibody dynamic analysis is presented. The complexity of scheduling parallel computations for a multibody dynamic analysis is studied. The problem of finding a shortest critical branch spanning tree is described and transformed to a minimum radius spanning tree, which is solved by an algorithm of polynomial complexity. T...

The paper aims at segmenting an image. The goal of image segmentation is to simplify and/or change the representation of an image into something that is more meaningful and simpler to analyze. In this paper we consider segmenting the image using the shortest spanning tree. To find the shortest spanning tree the image is first mapped into a graph. There have already been research conducted in th...

Classic inverse minimum spanning tree problem is to make the least edge weight modification such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. Although many applications can be formulated into this problem, fuzzy parameters are met in some real-world applications. In this paper, a type of inverse minimum spanning tree problem with fuzzy edge...

A linear-time algorithm for the minimum-ratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators. Disciplines Theory and Algorithms This article is available at Iowa State Univer...

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n ve...