Maximal Chains of Isomorphic Subgraphs of Countable Ultrahomogeneous Graphs
Logic
2017-09-26 v1 Combinatorics
Abstract
For a countable ultrahomogeneous graph G let P(G) denote the collection of domains of subgraphs of G isomorphic to G. The order types of maximal chains in the set P(G) U {\o} ordered by the inclusion are characterized as: (I) the order types of compact sets of reals having the minimum non-isolated, if G is the Rado graph or the Henson graph H_n, for some n>2; (II) the order types of compact nowhere dense sets of reals having the minimum non-isolated, if G is the union of \mu disjoint complete graphs of size \nu, where \mu \nu =\omega .
Keywords
Cite
@article{arxiv.1305.7080,
title = {Maximal Chains of Isomorphic Subgraphs of Countable Ultrahomogeneous Graphs},
author = {Milos S. Kurilic and Borisa Kuzeljevic},
journal= {arXiv preprint arXiv:1305.7080},
year = {2017}
}
Comments
13 pages. arXiv admin note: substantial text overlap with arXiv:1303.2828