# Sh:706

- Shelah, S. (2012).
*Universality among graphs omitting a complete bipartite graph*. Combinatorica,**32**(3), 325–362. arXiv: math/0102058 DOI: 10.1007/s00493-012-2033-4 MR: 2965281 -
Abstract:

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. - Current version: 2013-03-08_10 (35p) published version (38p)

Bib entry

@article{Sh:706, author = {Shelah, Saharon}, title = {{Universality among graphs omitting a complete bipartite graph}}, journal = {Combinatorica}, fjournal = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing}, volume = {32}, number = {3}, year = {2012}, pages = {325--362}, issn = {0209-9683}, doi = {10.1007/s00493-012-2033-4}, mrclass = {05C63 (03E04 03E35)}, mrnumber = {2965281}, mrreviewer = {P\'eter Komj\'ath}, doi = {10.1007/s00493-012-2033-4}, note = {\href{https://arxiv.org/abs/math/0102058}{arXiv: math/0102058}}, arxiv_number = {math/0102058} }