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Homomorphism-homogeneity classes of countable L-colored graphs
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SYSNO ASEP 0508590 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Homomorphism-homogeneity classes of countable L-colored graphs Author(s) Aranda, A. (DE)
Hartman, David (UIVT-O) RID, SAI, ORCIDSource Title Acta Mathematica Universitatis Comenianae. - : Univerzita Komenského v Bratislave - ISSN 0231-6986
Roč. 88, č. 3 (2019), s. 377-382Number of pages 6 s. Publication form Print - P Action EUROCOMB 2019. European Conference on Combinatorics, Graph Theory and Applications /9./ Event date 26.08.2019 - 30.08.2019 VEvent location Bratislava Country SK - Slovakia Event type EUR Language eng - English Country SK - Slovakia Keywords homomorphism-homogeneous ; monomorphism-homogeneous ; Rado graph ; classification ; Fraisse limit Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Open access Institutional support UIVT-O - RVO:67985807 UT WOS 000484349000004 EID SCOPUS 85073394451 Annotation The notion of homomorphism-homogeneity, introduced by Cameron and Nešetřil, originated as a variation on ultrahomogeneity. By fixing the type of finite homomorphism and global extension, several homogeneity classes, calledmorphism extension classes, can be defined. These classes are studied for various languages and axiom sets. Hartman, Hubička and Mašulović showed for finite undirected L-colored graphs without loops, where colors for vertices and edges are chosen from a partially ordered set L, that when L is a linear order, the classes HH and MH of L-colored graphs coincide, contributing thus to a question of Cameron and Nešetřil. They also showed that the same is true for vertex-uniform finite L-colored graphs when L is a diamond. In this work, we extend their results to countably infinite L-colored graphs, proving that the classes MH and HH coincide if and only if L is a linear order. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2020 Electronic address http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1224/669
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