On Halin-lattices in graphs

Halin [2] has shown that primitive sets with respect to a subset A of the vertex set of a connected graph G form a complete lattice (Halin-lattice). In this article special contractions are defined such that pairs (G, A) and these maps form a category HG and that a contravariant functor exists from HG to the category of complete lattices and lattice homomorphisms. Using this functor it is proved that the lattice homomorphism is a well-quasi ordering in the class of all Halin-lattices of rooted trees.

[1]  C. Nash-Williams.  On well-quasi-ordering infinite trees , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Michael Hager.  On Primitive Sets in Graphs , 1982, Eur. J. Comb..

[3]  Norbert Polat,et al.  Treillis de séparation des graphes , 1976 .

[4]  Gert Sabidussi.  Weak separation lattices of graphs , 1976 .

[5]  R. Halin,et al.  Über trennende Eckenmengen in Graphen und den Mengerschen Satz , 1964 .