Universal graphs with a forbidden subgraph: Block path solidity |
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| Authors: | Gregory Cherlin Saharon Shelah |
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| Affiliation: | 1.Department of Mathematics,Rutgers University,Rutgers,USA;2.Department of Mathematics,Hebrew University,Jerusalem,Israel;3.Rutgers University,Piscataway,USA |
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| 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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