@article{12563,
  abstract     = {he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems.},
  author       = {Krokhin, Andrei and Opršal, Jakub and Wrochna, Marcin and Živný, Stanislav},
  issn         = {1095-7111},
  journal      = {SIAM Journal on Computing},
  keywords     = {General Mathematics, General Computer Science},
  number       = {1},
  pages        = {38--79},
  publisher    = {Society for Industrial & Applied Mathematics},
  title        = {{Topology and adjunction in promise constraint satisfaction}},
  doi          = {10.1137/20m1378223},
  volume       = {52},
  year         = {2023},
}

@article{11991,
  abstract     = {The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been.},
  author       = {Krokhin, Andrei and Opršal, Jakub},
  issn         = {2372-3491},
  journal      = {ACM SIGLOG News},
  number       = {3},
  pages        = {30--59},
  publisher    = {Association for Computing Machinery},
  title        = {{An invitation to the promise constraint satisfaction problem}},
  doi          = {10.1145/3559736.3559740},
  volume       = {9},
  year         = {2022},
}