Two Fraïssé-style theorems for homomorphism-homogeneous relational structures

Thomas D. H. Coleman

doi:10.1016/j.disc.2019.111674

Two Fraïssé-style theorems for homomorphism-homogeneous relational structures

Thomas D. H. Coleman

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

14 Downloads (Pure)

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.

Original language	English
Article number	111674
Journal	Discrete Mathematics
Volume	343
Issue number	2
Early online date	3 Oct 2019
DOIs	https://doi.org/10.1016/j.disc.2019.111674
Publication status	Published - Feb 2020

Keywords

Homomorphism-homogeneous
Relational structures
Fraïssé theory
Infinite graph theory

Access to Document

10.1016/j.disc.2019.111674

FinalFraisseArticleSubmissionForDiscreteMathematics
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
Accepted author manuscript, 393 KBLicence: CC BY-NC-ND

Cite this

@article{c3dd29afba544bf1afaab33aec2839fb,

title = "Two Fra{\"i}ss{\'e}-style theorems for homomorphism-homogeneous relational structures",

abstract = "In this paper, we state and prove two Fra{\"i}ss{\'e}-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.",

keywords = "Homomorphism-homogeneous, Relational structures, Fra{\"i}ss{\'e} theory, Infinite graph theory",

author = "Coleman, {Thomas D. H.}",

year = "2020",

month = feb,

doi = "10.1016/j.disc.2019.111674",

language = "English",

volume = "343",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Two Fraïssé-style theorems for homomorphism-homogeneous relational structures

AU - Coleman, Thomas D. H.

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

KW - Homomorphism-homogeneous

KW - Relational structures

KW - Fraïssé theory

KW - Infinite graph theory

U2 - 10.1016/j.disc.2019.111674

DO - 10.1016/j.disc.2019.111674

M3 - Article

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

M1 - 111674

ER -

Two Fraïssé-style theorems for homomorphism-homogeneous relational structures

Abstract

Keywords

Access to Document

Fingerprint

Cite this