List Covering of Regular Multigraphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455444" target="_blank" >RIV/00216208:11320/22:10455444 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-031-06678-8_17" target="_blank" >https://doi.org/10.1007/978-3-031-06678-8_17</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-06678-8_17" target="_blank" >10.1007/978-3-031-06678-8_17</a>

Result language
angličtina
Original language name
List Covering of Regular Multigraphs
Original language description
A graph covering projection, also known as a locally bijective homomorphism, is a mapping between vertices and edges of two graphs which preserves incidencies and is a local bijection. This notion stems from topological graph theory, but has also found applications in combinatorics and theoretical computer science. It has been known that for every fixed simple regular graph H of valency greater than 2, deciding if an input graph covers H is NPcomplete. In recent years, topological graph theory has developed into heavily relying on multiple edges, loops, and semi-edges, but only partial results on the complexity of covering multigraphs with semi-edges are known so far. In this paper we consider the list version of the problem, called List-H-Cover, where the vertices and edges of the input graph come with lists of admissible targets. Our main result reads that the List-H-Cover problem is NP-complete for every regular multigraph H of valency greater than 2 which contains at least one semi-simple vertex (i.e., a vertex which is incident with no loops, with no multiple edges and with at most one semi-edge). Using this result we almost show the NP-co/polytime dichotomy for the computational complexity of ListH-Cover of cubic multigraphs, leaving just five open cases.
Czech name
—
Czech description
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Type
D - Article in proceedings
CEP classification
—
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/GA20-15576S" target="_blank" >GA20-15576S: Graph Covers: Symmetries and Complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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