What is the difference between spanning tree and spanning hypertree ?
2025-01-14 23:31:57.1736897517
What is the difference between spanning tree and spanning hypertree?
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A spanning a tree of a graph G is a subgraph T, that is a tree, and contains every vertex of $G$.
Define a hypergraph as a collection of nodes, and hyperedges, where hyperedges are collections of nodes that are grouped together. (Collections of size 2 are just edge).
A hypertree is a hypergraph that is connected and doesn't contain hyperedge cycles (that is a collection of hyper edges that loops around through the same sets of vertices).
A spanning hypertree of a hypergraph G,is simply a sub-hypergraph T, that is a hypertree and contains all the nodes of G.