{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T13:52:42Z","timestamp":1764251562119,"version":"3.41.0"},"reference-count":34,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T00:00:00Z","timestamp":1542758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000275","name":"The Leverhulme Trust","doi-asserted-by":"crossref","award":["RPG-2016-258"],"award-info":[{"award-number":["RPG-2016-258"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Theory"],"published-print":{"date-parts":[[2019,3,31]]},"abstract":"<jats:p>\n            The S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce\n            <jats:italic>endo-triviality<\/jats:italic>\n            , the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theoretic classifications of S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            in the case of reflexive\n            <jats:italic>digraphs<\/jats:italic>\n            . Chen (2014) proved, in the setting of constraint satisfaction problems, that S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            is NP-complete if H has the property that all of its polymorphisms are essentially unary. We give the first concrete application of his result by showing that every endo-trivial reflexive digraph H has this property. We then use the concept of endo-triviality to prove, as our main result, a dichotomy for S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            when H is a reflexive tournament: if H is transitive, then S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            is in NL; otherwise, it is NP-complete. By combining this result with some known and new results, we obtain a complexity classification for S\n            <jats:sc>urjective<\/jats:sc>\n            H-C\n            <jats:sc>olouring<\/jats:sc>\n            when H is a partially reflexive digraph of size at most 3.\n          <\/jats:p>","DOI":"10.1145\/3282431","type":"journal-article","created":{"date-parts":[[2018,11,26]],"date-time":"2018-11-26T13:07:25Z","timestamp":1543237645000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Surjective H-Colouring over Reflexive Digraphs"],"prefix":"10.1145","volume":"11","author":[{"given":"Beno\u00eet","family":"Larose","sequence":"first","affiliation":[{"name":"LACIM, Universit\u00e9 du Qu\u00e9bec a Montr\u00e9al, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Barnaby","family":"Martin","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Durham University, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dani\u00ebl","family":"Paulusma","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Durham University, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,11,21]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0401029"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2012.03.029"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1970398.1970400"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2017.37"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539700376676"},{"key":"e_1_2_1_6_1","volume-title":"Chemins et circuits Hamiltonians de graphes complets. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences Paris 249","author":"Camion Paul","year":"1959","unstructured":"Paul Camion . 1959. Chemins et circuits Hamiltonians de graphes complets. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences Paris 249 ( 1959 ), 2151--2152. Paul Camion. 1959. Chemins et circuits Hamiltonians de graphes complets. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences Paris 249 (1959), 2151--2152."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-014-0308-x"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2007.11.020"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1997.1812"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004939970003"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/1380681.1380685"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/1958204.1958205"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2006.02.009"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794266766"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-58741-7_26"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.06.039"},{"key":"e_1_2_1_17_1","doi-asserted-by":"crossref","unstructured":"Pavol Hell and Jaroslav Ne\u0161et\u0159il. 2004. Graphs and Homomorphisms. Oxford University Press.  Pavol Hell and Jaroslav Ne\u0161et\u0159il. 2004. Graphs and Homomorphisms. Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198528173.001.0001"},{"volume-title":"Contemporary Mathematics","author":"Hobby David Charles","key":"e_1_2_1_18_1","unstructured":"David Charles Hobby and Ralph McKenzie . 1988. The Structure of Finite Algebras , Contemporary Mathematics . American Mathematical Society . David Charles Hobby and Ralph McKenzie. 1988. The Structure of Finite Algebras, Contemporary Mathematics. American Mathematical Society."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.5555\/1141038.1705265"},{"key":"e_1_2_1_20_1","first-page":"1","article-title":"Taylor operations on finite reflexive structures","volume":"1","author":"Larose Benoit","year":"2006","unstructured":"Benoit Larose . 2006 . Taylor operations on finite reflexive structures . Int. J. Math. Comput. Sci. 1 , 1 (2006), 1 -- 26 . Benoit Larose. 2006. Taylor operations on finite reflexive structures. Int. J. Math. Comput. Sci. 1, 1 (2006), 1--26.","journal-title":"Int. J. Math. Comput. Sci."},{"key":"e_1_2_1_21_1","unstructured":"Benoit Larose. 2017. Algebra and the complexity of digraph CSPs: A survey. In The Constraint Satisfaction Problem: Complexity and Approximability. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik 267--285. http:\/\/drops.dagstuhl.de\/portals\/dfu\/index.php?semnr&equals;16027.  Benoit Larose. 2017. Algebra and the complexity of digraph CSPs: A survey. In The Constraint Satisfaction Problem: Complexity and Approximability. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik 267--285. http:\/\/drops.dagstuhl.de\/portals\/dfu\/index.php?semnr&equals;16027."},{"key":"e_1_2_1_22_1","volume-title":"A characterisation of first-order constraint satisfaction problems. Logical Methods Comput. 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Computational complexity of graph partition under vertex-compaction to an irreflexive hexagon. In Proceedings of the 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS\u201917). 69:1--69:14."},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2017.38"}],"container-title":["ACM Transactions on Computation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3282431","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3282431","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:57:29Z","timestamp":1750208249000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3282431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,21]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3,31]]}},"alternative-id":["10.1145\/3282431"],"URL":"https:\/\/doi.org\/10.1145\/3282431","relation":{},"ISSN":["1942-3454","1942-3462"],"issn-type":[{"type":"print","value":"1942-3454"},{"type":"electronic","value":"1942-3462"}],"subject":[],"published":{"date-parts":[[2018,11,21]]},"assertion":[{"value":"2018-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-09-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-21","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}