Definition:Spanning Tree/Creation
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Definition
There are two ways of creating a spanning tree for a given graph $G$:
Building-Up Method
Start with the edgeless graph $N$ whose vertices correspond with those of $G$.
Select edges of $G$ one by one, such that no cycles are created, and add them to $N$.
Continue till all vertices are included.
Cutting-Down Method
Start with the graph $G$.
Choose any cycle in $G$, and remove any one of its edges.
By Condition for Edge to be Bridge, this will not disconnect $G$.
Repeat this procedure till no cycles are left in $G$.
Also see
- Results about spanning trees can be found here.
Sources
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- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 4.1$: The Minimal Connector Problem: An Introduction to Trees