{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T21:12:26Z","timestamp":1774645946698,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T00:00:00Z","timestamp":1723680000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T00:00:00Z","timestamp":1723680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Korea Advanced Institute of Science and Technology"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2024,12]]},"abstract":"Abstract<\/jats:title>It is well-known that every tournament contains a Hamilton path, and every strongly connected tournament contains a Hamilton cycle. This paper establishes transversal<\/jats:italic> generalizations of these classical results. For a collection $$\\textbf{T}=(T_1,\\dots ,T_m)$$<\/jats:tex-math>\n \n T<\/mml:mi>\n =<\/mml:mo>\n (<\/mml:mo>\n \n T<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u22ef<\/mml:mo>\n ,<\/mml:mo>\n \n T<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of not-necessarily distinct tournaments on a common vertex set V<\/jats:italic>, an m<\/jats:italic>-edge directed graph $$\\mathcal {D}$$<\/jats:tex-math>\n D<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with vertices in V<\/jats:italic> is called a $$\\textbf{T}$$<\/jats:tex-math>\n T<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-transversal if there exists a bijection $$\\phi :E(\\mathcal {D})\\rightarrow [m]$$<\/jats:tex-math>\n \n \u03d5<\/mml:mi>\n :<\/mml:mo>\n E<\/mml:mi>\n (<\/mml:mo>\n D<\/mml:mi>\n )<\/mml:mo>\n \u2192<\/mml:mo>\n [<\/mml:mo>\n m<\/mml:mi>\n ]<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that $$e\\in E(T_{\\phi (e)})$$<\/jats:tex-math>\n \n e<\/mml:mi>\n \u2208<\/mml:mo>\n E<\/mml:mi>\n (<\/mml:mo>\n \n T<\/mml:mi>\n \n \u03d5<\/mml:mi>\n (<\/mml:mo>\n e<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for all $$e\\in E(\\mathcal {D})$$<\/jats:tex-math>\n \n e<\/mml:mi>\n \u2208<\/mml:mo>\n E<\/mml:mi>\n (<\/mml:mo>\n D<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We prove that for sufficiently large m<\/jats:italic> with $$m=|V|-1$$<\/jats:tex-math>\n \n m<\/mml:mi>\n =<\/mml:mo>\n |<\/mml:mo>\n V<\/mml:mi>\n |<\/mml:mo>\n -<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, there exists a $$\\textbf{T}$$<\/jats:tex-math>\n T<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-transversal Hamilton path. Moreover, if $$m=|V|$$<\/jats:tex-math>\n \n m<\/mml:mi>\n =<\/mml:mo>\n |<\/mml:mo>\n V<\/mml:mi>\n |<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and at least $$m-1$$<\/jats:tex-math>\n \n m<\/mml:mi>\n -<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the tournaments $$T_1,\\ldots ,T_m$$<\/jats:tex-math>\n \n \n T<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n ,<\/mml:mo>\n \n T<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are assumed to be strongly connected, then there is a $$\\textbf{T}$$<\/jats:tex-math>\n T<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-transversal Hamilton cycle. In our proof, we utilize a novel way of partitioning tournaments which we dub $$\\textbf{H}$$<\/jats:tex-math>\n H<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-partition<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/s00493-024-00123-1","type":"journal-article","created":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T09:02:24Z","timestamp":1723712544000},"page":"1381-1400","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hamilton Transversals in Tournaments"],"prefix":"10.1007","volume":"44","author":[{"given":"Debsoumya","family":"Chakraborti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaehoon","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hyunwoo","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaehyeon","family":"Seo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,15]]},"reference":[{"key":"123_CR1","doi-asserted-by":"publisher","unstructured":"Aharoni, R., DeVos, M., de la Maza, S. 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