The maximum internal spanning tree (MIST) problem is utilized to determine a in graph G, with the number of possible vertices. incremental (IMIST) version MIST whose feasible solutions are edge-sequences e1, e2, …, en−1 such that first k edges form trees for all ∈ [n − 1]. A solution’s quality measured using $${\text{max}_{k \in - 1]}}\frac{{\text{opt}(G,k)}}{{\left| {\text{In}({T_k})} \right|}...

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the p...

We present a general framework for obtaining efficient algorithms for computing minimum spanning trees. We use this framework to derive the classical algorithms of Prim, Kruskal and Bor̊uvka. We then describe the randomized linear-time algorithm of Karger, Klein and Tarjan. The algorithm of Karger, Klein and Tarjan uses deterministic linear-time implementations of a verification algorithm of Kom...