Homomorphisms between graphs embedded in surfaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10492674" target="_blank" >RIV/00216208:11320/24:10492674 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7YqIMKUtpg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7YqIMKUtpg</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2024.103936" target="_blank" >10.1016/j.ejc.2024.103936</a>

Result language
angličtina
Original language name
Homomorphisms between graphs embedded in surfaces
Original language description
We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the combinatorial structure (as a graph homomorphism) and the topological structure of the surface (in particular, orientability and genus). Notions such as the core of a graph and the homomorphism order on cores are then extended to maps. We also develop a purely combinatorial framework for various topological features of a map such as the contractibility of closed walks, which in particular allows us to characterize map cores. We then show that the poset of map cores ordered by the existence of a homomorphism is connected and, in contrast to graph homomorphisms, does not contain any dense interval (so it is not universal for countable posets). Finally, we give examples of a pair of cores with an infinite number of cores between them, an infinite chain of gaps, and arbitrarily large antichains with a common homomorphic image. (c) 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA22-17398S" target="_blank" >GA22-17398S: Flows and cycles in graphs on surfaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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