An 
-thin tree in a finite
connected graph 
is a spanning tree 
such that 
for every
vertex subset 
, where 
is the cut consisting of graph edges with one endpoint in 
. In a multigraph, parallel
graph edges are counted with
multiplicity.
Thin Tree
See also
Cut, Edge Connectivity, Multigraph, Spanning TreeExplore with Wolfram|Alpha
References
Klein, N.; Olver, N.; and Yeoh, Z. S. "Thin Trees for Near Minimum Cuts." In Proc. 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026) (Ed. S. Bhattacharya, D. Nanongkai, M. Benedikt, and G. Puppis). Dagstuhl, Germany: Schloss Dagstuhl-Leibniz-Zentrum für Informatik, pp. 129:1-129:18, 2026. https://doi.org/10.4230/LIPIcs.ICALP.2026.129.Cite this as:
Weisstein, Eric W. "Thin Tree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThinTree.html