# Gomory‐Hu trees of infinite graphs with finite total weight

Gomory‐Hu trees of infinite graphs with finite total weight A well‐known theorem of Gomory and Hu states that if G is a finite graph with nonnegative weights on its edges, then there exists a tree T (now called a Gomory‐Hu tree) on V(G) such that for all u≠v∈V(G) there is an e∈E(T) such that the two components of T−e determine an optimal (minimal valued) cut between u an v in G. In this article, we extend their result to infinite weighted graphs with finite total weight. Furthermore, we show by an example that one cannot omit the condition of the finiteness of the total weight. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Graph Theory Wiley

# Gomory‐Hu trees of infinite graphs with finite total weight

, Volume 88 (1) – Jan 1, 2018
10 pages

/lp/wiley/gomory-hu-trees-of-infinite-graphs-with-finite-total-weight-50LdNc0kee
Publisher
Wiley
ISSN
0364-9024
eISSN
1097-0118
D.O.I.
10.1002/jgt.22207
Publisher site
See Article on Publisher Site

### Abstract

A well‐known theorem of Gomory and Hu states that if G is a finite graph with nonnegative weights on its edges, then there exists a tree T (now called a Gomory‐Hu tree) on V(G) such that for all u≠v∈V(G) there is an e∈E(T) such that the two components of T−e determine an optimal (minimal valued) cut between u an v in G. In this article, we extend their result to infinite weighted graphs with finite total weight. Furthermore, we show by an example that one cannot omit the condition of the finiteness of the total weight.

### Journal

Journal of Graph TheoryWiley

Published: Jan 1, 2018

Keywords: ; ; ;

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