Lattice betweenness relation and a generalization of König's lemma
Jarmila Hedlı́ková, Tibor Katriňák · Czech digital mathematics library · 1996
A tree is a partially ordered set (T, -partite Konig graph G with finite parts contains an uj-frame.We present an extension of Konig's lemma which has the origin in a character ization of lattices by a ternary relation (the lattice betweenness relation) given by M. Kolibiar.Our generalization of Konig's lemma states that for every up-directed partially ordered set S, each transitive S-partite Konig graph G with sufficiently many finite parts contains an S-frame.As an example, we apply tliis result in lattice theory A MS Subject Classification (1991): Primary 06A06, 05C20, 06B05, 08A02.