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Weak Separation Lattices of Graphs

Published online by Cambridge University Press:  20 November 2018

Gert Sabidussi
Gert Sabidussi*
Affiliation:
Université de Montréal, Montréal, Quebec
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In an interesting, but apparently largely unknown, paper [1] Halin has introduced the concept of a primitive set of vertices of a graph. This concept, or rather a slight modification of it, seems to provide the key to a new approach to the wrell-known and important class of graph-theoretical problems centering on the notion of separation. As is well known, if A, B, C are sets of vertices of a (non-oriented) graph X, C is said to separate A and B if and only if every AB-path in X contains a vertex of C.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 691 - 724
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Halin, R., Uber trennende Eckenmengen in Graphen und den Mengerschen Satz, Math. Ann. 157 (1964), 34–41.Google Scholar
2. Harary, F., Graph theory (Addison-Wesley, Reading, Mass., 1969).Google Scholar
3. Mercier, C., Treillis de séparation des graphes, Mémoire de maîtrise, Université de Montréal, Septembre 1972.Google Scholar
4. Ore, O., Theory of graphs, Amer. Math. Soc. Colloq. Publ. 38 (Providence, R.I., 1962).Google Scholar
5. Polat, N., Treillis de séparation des graphes, Can. J. Math. 28 (1976), 725–752.Google Scholar
6. Pym, J. S. and Hazel Perfect, Submodular functions and independence structures, J. Math. Anal. Appl. 30 (1970), 1–31.Google Scholar