Computational Complexity of Covering Colored Mixed Multigraphs with Degree Partition Equivalence Classes of Size at Most Two (Extended Abstract)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10474472" target="_blank" >RIV/00216208:11320/23:10474472 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-031-43380-1_8" target="_blank" >https://doi.org/10.1007/978-3-031-43380-1_8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-43380-1_8" target="_blank" >10.1007/978-3-031-43380-1_8</a>
Alternative languages
Result language
angličtina
Original language name
Computational Complexity of Covering Colored Mixed Multigraphs with Degree Partition Equivalence Classes of Size at Most Two (Extended Abstract)
Original language description
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph H, the H-Cover problem asks if an input graph G allows a graph covering projection onto H. Despite the fact that the quest for characterizing the computational complexity of H-Cover had been started more than 30 years ago, only a handful of general results have been known so far. In this paper, we present a complete characterization of the computational complexity of covering colored graphs for the case that every equivalence class in the degree partition of the target graph has at most two vertices. We prove this result in a very general form. Following the lines of current development of topological graph theory, we study graphs in the most relaxed sense of the definition - the graphs are mixed (they may have both directed and undirected edges), may have multiple edges, loops, and semi-edges. We show that a strong P/NP-co dichotomy holds true in the sense that for each such fixed target graph H, the H-Cover problem is either polynomial time solvable for arbitrary inputs, or NP-complete even for simple input graphs.
Czech name
—
Czech description
—
Classification
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)
Result continuities
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)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISBN
978-3-031-43379-5
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
15
Pages from-to
101-115
Publisher name
Springer Nature
Place of publication
Cham
Event location
Fribourg, Switzerland
Event date
Jun 28, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—