Universal graphs with a forbidden subtree

  title={Universal graphs with a forbidden subtree},
  author={Gregory L. Cherlin and Saharon Shelah},
  journal={J. Comb. Theory, Ser. B},
  • G. Cherlin, S. Shelah
  • Published 10 December 2005
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
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. 
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