Sh:850

• Cherlin, G. L., & Shelah, S. (2007). Universal graphs with a forbidden subtree. J. Combin. Theory Ser. B, 97(3), 293–333. arXiv: math/0512218 DOI: 10.1016/j.jctb.2006.05.008 MR: 2305886
• Abstract:
  We show that the problem of the existence of universal graphs with specified forbidden subgraphs can be systematically reduced to certain critical cases by a simple pruning technique which simplifies the underlying structure of the forbidden graphs, viewed as trees of blocks. As an application, we characterize the trees T for which a universal countable T-free graph exists.
• Version 2006-05-24_11 (57p) published version (41p)

@article{Sh:850,
 author = {Cherlin, Gregory L. and Shelah, Saharon},
 title = {{Universal graphs with a forbidden subtree}},
 journal = {J. Combin. Theory Ser. B},
 fjournal = {Journal of Combinatorial Theory. Series B},
 volume = {97},
 number = {3},
 year = {2007},
 pages = {293--333},
 issn = {0095-8956},
 mrnumber = {2305886},
 mrclass = {03C15 (05C05)},
 doi = {10.1016/j.jctb.2006.05.008},
 note = {\href{https://arxiv.org/abs/math/0512218}{arXiv: math/0512218}},
 arxiv_number = {math/0512218}
}