Stefan Bard ; Thomas Bellitto ; Christopher Duffy ; Gary MacGillivray ; Feiran Yang - Complexity of locally-injective homomorphisms to tournaments

dmtcs:4021 - Discrete Mathematics & Theoretical Computer Science, November 30, 2018, vol. 20 no. 2 - https://doi.org/10.23638/DMTCS-20-2-4
Complexity of locally-injective homomorphisms to tournamentsArticle

Authors: Stefan Bard ; Thomas Bellitto ; Christopher Duffy ORCID; Gary MacGillivray ; Feiran Yang

    For oriented graphs $G$ and $H$, a homomorphism $f: G \rightarrow H$ is locally-injective if, for every $v \in V(G)$, it is injective when restricted to some combination of the in-neighbourhood and out-neighbourhood of $v$. Two of the possible definitions of local-injectivity are examined. In each case it is shown that the associated homomorphism problem is NP-complete when $H$ is a reflexive tournament on three or more vertices with a loop at every vertex, and solvable in polynomial time when $H$ is a reflexive tournament on two or fewer vertices.


    Volume: vol. 20 no. 2
    Section: Graph Theory
    Published on: November 30, 2018
    Accepted on: September 3, 2018
    Submitted on: October 27, 2017
    Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics,05C15
    Funding:
      Source : OpenAIRE Graph
    • Funder: Natural Sciences and Engineering Research Council of Canada

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