Universal graphs with a forbidden subgraph: Block path solidity
Combinatorics
2014-04-24 v1
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 Furedi and Komjath, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph.
Cite
@article{arxiv.1404.5757,
title = {Universal graphs with a forbidden subgraph: Block path solidity},
author = {Gregory Cherlin and Saharon Shelah},
journal= {arXiv preprint arXiv:1404.5757},
year = {2014}
}