{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:06Z","timestamp":1740144486644,"version":"3.37.3"},"reference-count":22,"publisher":"EDP Sciences","issue":"2","license":[{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"vor","delay-in-days":46,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,3,4]]},"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p>We study the (<jats:italic>a, b<\/jats:italic>)-monochromatic transversal game that is a combinatorial Maker\u2013Breaker game where Alice and Bob alternately colour <jats:italic>a<\/jats:italic> vertices in red and <jats:italic>b<\/jats:italic> vertices in blue of a hypergraph, respectively. Either player is enabled to start the game. Alice tries to construct a hyperedge transversal, and Bob tries to prevent this. The winner is Alice if she obtains a red hyperedge transversal; otherwise, Bob wins the game if he obtains a monochromatic blue hyperedge. Maker\u2013Breaker games were determined to be PSPACE-complete. In this work, we analyze the game played on clique-hypergraphs of powers of cycles, and we show strategies that, depending on the choice of the parameters, allow a specific player to win the game.<\/jats:p>","DOI":"10.1051\/ro\/2024054","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T19:55:29Z","timestamp":1709754929000},"page":"1759-1770","source":"Crossref","is-referenced-by-count":0,"title":["The (<i>a, b<\/i>)-monochromatic transversal game on clique-hypergraphs of powers of cycles"],"prefix":"10.1051","volume":"58","author":[{"given":"Wilder P.","family":"Mendes","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8340-4881","authenticated-orcid":false,"given":"Simone","family":"Dantas","sequence":"additional","affiliation":[]},{"given":"Sylvain","family":"Gravier","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1016\/j.dam.2010.05.003","volume":"159","author":"Andres","year":"2011","journal-title":"Discrete Appl. Math"},{"key":"R2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1137\/S0895480199359995","volume":"17","author":"Bacs\u00f3","year":"2004","journal-title":"SIAM J. Discrete Math"},{"key":"R3","unstructured":"Berge C., Hypergraphs: Combinatorics of Finite Sets, 1st edition. North-Holland, Amsterdam (1989)."},{"key":"R4","unstructured":"Berlekamp E.R., Conway J.H. and Guy R.K., Winning Ways for Your Mathematical Plays: Volume 1 and 2, 1st edition. A. K. Peters Press, Natick (1981)."},{"key":"R5","doi-asserted-by":"crossref","first-page":"1830","DOI":"10.1137\/15M1049361","volume":"30","author":"Bujt\u00e1s","year":"2016","journal-title":"SIAM J. Discrete Math"},{"key":"R6","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ejc.2016.07.003","volume":"59","author":"Bujt\u00e1s","year":"2017","journal-title":"Eur. J. Comb"},{"key":"R7","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1007\/s00373-012-1241-4","volume":"29","author":"Campos","year":"2013","journal-title":"Graphs Comb"},{"key":"R8","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.dam.2016.03.014","volume":"208","author":"Dorbec","year":"2016","journal-title":"Discrete Appl. Math"},{"key":"R9","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1051\/ro\/2009029","volume":"43","author":"Duch^ene","year":"2009","journal-title":"RAIRO: Oper. Res"},{"key":"R10","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0097-3165(91)90009-6","volume":"57","author":"Duffus","year":"1991","journal-title":"J. Comb. Theory Ser. A"},{"key":"R11","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10479-007-0189-x","volume":"157","author":"Dur\u00e1n","year":"2008","journal-title":"Ann. Oper. Res"},{"key":"R12","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0097-3165(73)90005-8","volume":"14","author":"Erd\u0151s","year":"1973","journal-title":"J. Comb. Theory Ser. A"},{"key":"R13","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0012-365X(92)90681-5","volume":"108","author":"Erd\u0151s","year":"1992","journal-title":"Discrete Math"},{"key":"R14","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.entcs.2019.08.041","volume":"346","author":"Furtado","year":"2019","journal-title":"Electron. Notes Theor. Comput. Sci"},{"key":"R15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/S0012-365X(03)00197-3","volume":"272","author":"Gravier","year":"2003","journal-title":"Discrete Math"},{"key":"R16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1051\/ro\/2011112","volume":"45","author":"Groshaus","year":"2011","journal-title":"RAIRO: Oper. Res"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Hefetz D., Krivelevich M., Stojakovi\u0107 M. and Szab\u00f3 T., Positional Games. Birkh\u00a8auser\/Springer, Basel (2014).","DOI":"10.1007\/978-3-0348-0825-5"},{"key":"R18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00493-015-3316-3","volume":"37","author":"Henning","year":"2017","journal-title":"Combinatorica"},{"key":"R19","unstructured":"Meidanis J., Edge coloring of cycle powers is easy (1998). Unpublished manuscript http:\/\/www.ic.unicamp.br\/~meidanis\/ last visited 05\/10\/2022."},{"key":"R20","doi-asserted-by":"crossref","unstructured":"Oliveira D.L., Dantas S. and Luiz A.G., Results on the graceful game and range-relaxed graceful game, in XI European Conference on Combinatorics, Graph Theory and Applications (EuroComb 21), 2021, Barcelona. Trends in Mathematics: Research Perspectives CRM Barcelona. Vol. 14. Springer, Switzerland (2021) 214\u2013220.","DOI":"10.1007\/978-3-030-83823-2_34"},{"key":"R21","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0022-0000(78)90045-4","volume":"16","author":"Schaefer","year":"1978","journal-title":"J. Comput. Syst. Sci"},{"key":"R22","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1051\/ro\/2013035","volume":"47","author":"Torres","year":"2013","journal-title":"RAIRO: Oper. Res"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024054\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T08:14:00Z","timestamp":1713255240000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3]]},"references-count":22,"journal-issue":{"issue":"2"},"alternative-id":["ro220675"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2024054","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2024,3]]}}}