Degree Bounded Spanning Trees

Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

In this paper, we present some new results describing connections between the spectrum of a regular graph and its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.

A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees

A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees

A sufficient condition for spanning trees with bounded maximum degree in a graph

Large Bounded Degree Trees in Expanding Graphs

A remarkable result of Friedman and Pippenger [4] gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. Haxell [5] showed that under slightly stronger assumptions on the expansion rate, their technique allows one to find arbitrarily large trees with bounded maximum degree. Using a slightly weaker version of Haxell’s result we...

Spanning Trees of Bounded Degree Graphs

We consider lower bounds on the number of spanning trees of connected graphs with degree bounded by d. The question is of interest because such bounds may improve the analysis of the improvement produced by memorisation in the runtime of exponential algorithms. The value of interest is the constant βd such that all connected graphs with degree bound ed by d have at least β d spanning trees wher...