This paper addresses the following questions for a given tree T and integer d 2: (1) What is the minimum number of degree-d subtrees that partition E(T)? (2) What is the minimum n...
In the MINIMUM BOUNDED DEGREE SPANNING TREE problem, we are given an undirected graph with a degree upper bound Bv on each vertex v, and the task is to find a spanning tree of min...
In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for eve...
The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, nding the smallest graph G in C that allows a traverse of all edge...
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...