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Minimization Problems for Infinite n-Connected Graphs

Published online by Cambridge University Press:  12 September 2008

R. Halin
R. Halin
Affiliation:
Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, D-20146, Hamburg, Germany
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Abstract

A graph G is called n-minimizable if it can be reduced, by deleting a set of its edges, to a minimally n-connected graph. It is shown that, if n-connected graphs G and H differ only by finitely many vertices and edges, then G is n-minimizable if and only if H is n-minimizable (Theorem 4.12). In the main result, conditions are given that a tree decomposition of an n-connected graph G must satisfy in order to guarantee that the n-minimizability of each of the members of this decomposition implies the n-minimizability of the graph G (Theorem 6.5).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 4 , December 1993 , pp. 417 - 436
Copyright
Copyright © Cambridge University Press 1993

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