## Bard, Stefan and Bellitto, Thomas and Duffy, Christopher and MacGillivray, Gary and Yang, Feiran - 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 tournaments

Authors: Bard, Stefan and Bellitto, Thomas and Duffy, Christopher and MacGillivray, Gary and Yang, Feiran

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
Submitted on: October 27, 2017
Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics,05C15

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