Two criteria for an edge to belong to all MSTs
Let $ G$ be a connected undirected graph, with integral positive weights on the edges, and let $ e_1$ be an edge of $ G$ . As part of an assignment I proved the following Lemma 1: The edge $ e_1$...
View Articleproof that multiple minimum spanning trees (MSTs) for a given edge- weighted...
How do we prove this? I thought we could use safe edge property and say if the edges were different, the safe edge property would choose only the minimum weight edge, but since there are multiple...
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Sorting vertices by MST in a forest of MSTs
Consider a number of vertices. They are separated into a number of MSTs (so there’s a forest of MSTs) using Kruskal’s algorithm. For each vertex I need to know in which MST they are located. Each MST...
View ArticleTelling Probability of Point Configurations being in Convex Configuration...
Question: what is the probability that four distinct points in general position in the Euclidean plane are in convex configuration, depending on the number of leaf nodes in their MST? I assume that a...
View ArticleMSTP: choice of MSTs and “freezing” an active topology
The scenario: A network topology consiting of a few layer 2 switches with some end devices on the edges. The pairs of end devices are in the same VLAN, a spanning tree protocol like MSTP created...
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