Two Fraïssé-style theorems for homomorphism-homogeneous relational structures

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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.
Original languageEnglish
Article number111674
JournalDiscrete Mathematics
Issue number2
Early online date3 Oct 2019
Publication statusPublished - Feb 2020


  • Homomorphism-homogeneous
  • Relational structures
  • Fraïssé theory
  • Infinite graph theory


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