A spanning subgraph of a graph 
is a subgraph with the same vertex set as 
. Its edge
set may be any subset of the edge
set of 
. An acyclic spanning
subgraph is a spanning forest, and a connected acyclic spanning subgraph with at least one vertex
is a spanning tree (Wu et al. 2026).
Spanning Subgraph
See also
Spanning Forest, Spanning Tree, SubgraphExplore with Wolfram|Alpha
References
Wu, T.; Lu, S.; and Dong, X. "A Sharp Upper Bound on the Number of Spanning Forests of Regular Graphs." 5 Oct 2026. https://arxiv.org/abs/2610.05722.Cite this as:
Weisstein, Eric W. "Spanning Subgraph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SpanningSubgraph.html