Spanning tree

algorithm for finding the minimum spanning tree for weighted undirected graphs

network protocol that builds a loop-free logical topology for Ethernet networks

data structure, subgraph of a weighted graph

minimum spanning forest algorithm that greedily adds edges

subgraph of an undirected graph G that is a tree which includes all of the vertices of G

arrangement of joined polytopes which can be folded to become the facets of a higher-dimensional polytope

algorithm for finding minimum spanning trees by repeatedly finding the shortest edge out of each subtree in a forest and adding all such edges to the forest

algorithm that approximates solutions to the travellng salesman problem on a metric space, guaranteeing that its solutions will be within 1½ of the optimal solution length; discovered by Nicos Christofides in 1976

theorem of computing the number of spanning trees in a graph

the minimum number of edges to remove from a graph to eliminate all its cycles

The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to cover all the edges of the graph. The Nash-Williams theorem provides necessary and sufficient conditions for when a graph is k-arboric.

minimum spanning forest algorithm that greedily deletes edges

matroid whose independent sets are forests in an undirected graph

the shortest network collecting a given set of points in the plane

spanning tree consisting of shortest paths from a vertex