Universality among the graph omitting a complete bipartite graph

Details Universality among the graph omitting a complete bipartite graph Universality among the graph omitting a complete bipartite graph

2001-02-07

arxiv.org/abs/math/0102058v2

Mathematics

Logic

Scientific paper

For cardinals lambda, kappa, theta we consider the class of graphs of cardinality lambda which has no subgraph which is (kappa, theta)-complete bipartite graph. The question is whether in such a class there is a universal one under (weak) embedding. We solve this problem completely under GCH. Under various assumptions mostly related to cardinal arithmetic we prove nonexistence of universals for this problem and some related ones.

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