Simplicial minors and decompositions of graphs
Published online by Cambridge University Press: 24 October 2008
Extract
The purpose of this paper is to give natural characterizations of the countable graphs that admit tree-decompositions or simplicial tree-decompositions into primes. Tree-decompositions were recently introduced by Robertson and Seymour in their series of papers on graph minors [7]. Simplicial tree-decompositions were first considered by Halin[6], being the most typical kind of ‘simplicial decomposition’ as introduced by Halin[5] in 1964. The problem of determining which infinite graphs admit a simplicial decomposition into primes has stood unresolved since then; a first solution for simplicial tree-decompositions was given in [2].
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 409 - 426
- Copyright
- Copyright © Cambridge Philosophical Society 1988
References
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