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Questions tagged [spanning-tree]

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1
vote
0answers
30 views

Packing low-depth spanning trees in a bi-clique

A bi-clique of order $n$ (denoted by $B_n$) is a complete bipartite graph with each side having $n$ nodes. A packing of spanning trees of $B_n$ is a collection of edge-disjoint spanning trees of $B_n$....
9
votes
0answers
131 views

How to sample a lot of independent uniform spanning trees?

There are a bunch of good algorithms for sampling a uniform spanning tree from a graph $G$. For example, Aldous/Broder and Wilson's algorithm are pretty efficient. However, each of these graphs only ...
5
votes
2answers
174 views

Minimising the root-set of a spanning hyperforest of a hypergraph

I am interested in the complexity of a problem involving spanning hyperforests (a union of hypertrees, which covers all of the vertices) of a $k$-hypergraph. I describe the relevant definitions for ...
2
votes
1answer
65 views

Are equally weighted MSTs closely related?

Suppose we have an undirected connected graph $G=(V,E)$ that has several minimum spanning trees. We say two trees $T_1, T_2$ are connected if they share exactly $|V|-2$ edges(*). In other words $T_1$ ...
4
votes
0answers
126 views

Girth of graphs that decompose into two disjoint union of spanning trees

Let $G$ be an $n$-node graph that can be decomposed into two disjoint union of spanning trees. In particular, $G$ has $2n-2$ edges. It is not hard to show that the girth of $G$ is at most $O(\log n)...