Affiliation:
1. Katedra Aplikované Matematiky , Univerzita Karlova , Malostranské Náměstí 25 , Praha , Czech Republic
Abstract
Abstract
Let XY
L,T
consist of all countable L-structures M that satisfy the axioms T and in which all homomorphisms of type X (these could be plain homomorphisms, monomorphisms, or isomorphisms) between finite substructures of M are restrictions of an endomorphism of M of type Y (for example, an automorphism or a surjective endomorphism). Lockett and Truss introduced 18 such classes for relational structures. For a given pair L, T however, two or more morphism-extension properties may define the same class of structures.
In this paper, we establish all equalities and inequalities between morphism-extension classes of countable graphs.
Reference14 articles.
1. Aranda, A.—Hartman, D.: The independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs, European J. Combin. 85 (2020).
2. Aranda, A.: IB-homogeneous graphs, Discrete Math., to appear, available at https://arxiv.org/abs/1909.02920.
3. Cameron, P. J.—Nešetřil, J.: Homomorphism-homogeneous relational structures, Combin. Probab. Comput. 15(1–2) (2006), 91–103.
4. Cameron, P. J.: Oligomorphic Permutation Groups. LMS Lecture Note Series 152, 2008.
5. Coleman, T. D. H.—Evans, D. M.—gray, R. D.: MB-homogeneity for graphs and relational structures, European J. Combin. 78 (2019), 163–189.