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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