Universal graphs with a forbidden subgraph: Block path solidity

Abstract

Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Füredi and Komjáth, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph.

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Correspondence to Gregory Cherlin.

Additional information

First author supported by NSF Grant DMS-1101597.

The second author would like to thank the NSF, grant no. DMS 1101597, for support of this paper. Publication 1033.

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Cherlin, G., Shelah, S. Universal graphs with a forbidden subgraph: Block path solidity. Combinatorica 36, 249–264 (2016). https://doi.org/10.1007/s00493-014-3181-5

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Mathematics Subject Classification (2010)

  • 05C60
  • 05C63
  • 03C15