Two Fraïssé-style theorems for homomorphism-homogeneous relational structures
Abstract
In this paper, we state and prove two Fraïssé-style results that cover existence and uniqueness properties for twelve of the eighteen different notions of homomorphism-homogeneity as introduced by Lockett and Truss, and provide forward directions and implications for the remaining six cases. Following these results, we completely determine the extent to which the countable homogeneous undirected graphs (as classified by Lachlan and Woodrow) are homomorphism-homogeneous; we also provide some insight into the directed graph case.
Citation
Coleman , T D H 2020 , ' Two Fraïssé-style theorems for homomorphism-homogeneous relational structures ' , Discrete Mathematics , vol. 343 , no. 2 , 111674 . https://doi.org/10.1016/j.disc.2019.111674
Publication
Discrete Mathematics
Status
Peer reviewed
ISSN
0012-365XType
Journal article
Rights
Copyright © 2019 Elsevier B.V. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.disc.2019.111674
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