English

QCSP on Reflexive Tournaments

Computational Complexity 2022-04-13 v2

Abstract

We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components H_1,...,H_n so that there exists an edge from every vertex of H_i to every vertex of H_j if and only if i<j. We prove that if H has both its initial and final strongly connected component (possibly equal) of size 1, then QCSP(H) is in NL and otherwise QCSP(H) is NP-hard.

Cite

@article{arxiv.2104.10570,
  title  = {QCSP on Reflexive Tournaments},
  author = {Benoit Larose and Petar Markovic and Barnaby Martin and Daniel Paulusma and Siani Smith and Stanislav Zivny},
  journal= {arXiv preprint arXiv:2104.10570},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:1709.09486

R2 v1 2026-06-24T01:24:08.259Z