# Spanning trees with few branch vertices

@article{DeBiasio2019SpanningTW,
title={Spanning trees with few branch vertices},
author={Louis DeBiasio and Allan Lo},
journal={ArXiv},
year={2019},
volume={abs/1709.04937}
}
• Published in SIAM J. Discrete Math. 2019
• Mathematics, Computer Science
• A branch vertex in a tree is a vertex of degree at least three. We prove that for all positive integers $s$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch vertices. Asymptotically, this is best possible and solves a problem of Flandrin, Kaiser, Kuuzel, Li and Ryjaucek, which was originally motivated by an optimization problem in the design of optical networks.

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## Matchings with few colors in colored complete graphs and hypergraphs

• Mathematics
• 2020
VIEW 1 EXCERPT
CITES METHODS

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 32 REFERENCES

## Monochromatic cycle partitions of graphs with large minimum degree

• Mathematics, Computer Science
• J. Comb. Theory, Ser. B
• 2014
VIEW 5 EXCERPTS

## A Dirac-Type Theorem for 3-Uniform Hypergraphs

• Computer Science, Mathematics
• Comb. Probab. Comput.
• 2006
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## Independence trees and Hamilton cycles

• Mathematics
• 1998
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

## Spanning spiders and light-splitting switches

• Computer Science, Mathematics
• Discret. Math.
• 2004
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## A branch-and-cut algorithm for the minimum branch vertices spanning tree problem

• Computer Science, Mathematics
• Comput. Oper. Res.
• 2017
VIEW 1 EXCERPT

## Decomposition methods based on articulation vertices for degree-dependent spanning tree problems

• Mathematics, Computer Science
• Comp. Opt. and Appl.
• 2017
VIEW 1 EXCERPT

## An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices

• Computer Science, Mathematics
• Comp. Opt. and Appl.
• 2016
VIEW 1 EXCERPT

## Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem

VIEW 1 EXCERPT

## An edge-swap heuristic for generating spanning trees with minimum number of branch vertices

VIEW 1 EXCERPT

## Approximating Spanning Trees with Few Branches

• Mathematics, Computer Science
• Theory of Computing Systems
• 2014
VIEW 1 EXCERPT