{"author":[{"last_name":"Krokhin","full_name":"Krokhin, Andrei","first_name":"Andrei"},{"last_name":"Opršal","full_name":"Opršal, Jakub","id":"ec596741-c539-11ec-b829-c79322a91242","first_name":"Jakub","orcid":"0000-0003-1245-3456"},{"first_name":"Marcin","last_name":"Wrochna","full_name":"Wrochna, Marcin"},{"full_name":"Živný, Stanislav","last_name":"Živný","first_name":"Stanislav"}],"year":"2023","type":"journal_article","volume":52,"date_updated":"2023-08-01T13:11:30Z","month":"01","page":"38-79","date_created":"2023-02-16T07:03:52Z","keyword":["General Mathematics","General Computer Science"],"department":[{"_id":"UlWa"}],"title":"Topology and adjunction in promise constraint satisfaction","_id":"12563","intvolume":"        52","publication_status":"published","oa":1,"oa_version":"Preprint","isi":1,"acknowledgement":"Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\u001eects only the authors’ views and not the views of the ERC or the European Commission. ","article_type":"original","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2003.11351","open_access":"1"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"date_published":"2023-01-01T00:00:00Z","ec_funded":1,"status":"public","day":"01","publication":"SIAM Journal on Computing","external_id":{"arxiv":["2003.11351"],"isi":["000955000000001"]},"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"1","language":[{"iso":"eng"}],"article_processing_charge":"No","abstract":[{"lang":"eng","text":"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."}],"publisher":"Society for Industrial & Applied Mathematics","citation":{"short":"A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79.","apa":"Krokhin, A., Opršal, J., Wrochna, M., &#38; Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/20m1378223\">https://doi.org/10.1137/20m1378223</a>","mla":"Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” <i>SIAM Journal on Computing</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics, 2023, pp. 38–79, doi:<a href=\"https://doi.org/10.1137/20m1378223\">10.1137/20m1378223</a>.","ista":"Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79.","ieee":"A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” <i>SIAM Journal on Computing</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics, pp. 38–79, 2023.","ama":"Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. <i>SIAM Journal on Computing</i>. 2023;52(1):38-79. doi:<a href=\"https://doi.org/10.1137/20m1378223\">10.1137/20m1378223</a>","chicago":"Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/20m1378223\">https://doi.org/10.1137/20m1378223</a>."},"scopus_import":"1","doi":"10.1137/20m1378223"}