{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T23:20:50Z","timestamp":1776900050489,"version":"3.51.2"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T00:00:00Z","timestamp":1748563200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In this paper, we study discrepancy questions for spanning subgraphs of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline1.png\"\/>\n                        <jats:tex-math>$k$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -uniform hypergraphs. Our main result is that, for any integers\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline2.png\"\/>\n                        <jats:tex-math>$k \\ge 3$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline3.png\"\/>\n                        <jats:tex-math>$r \\ge 2$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , any\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline4.png\"\/>\n                        <jats:tex-math>$r$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -colouring of the edges of a\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline5.png\"\/>\n                        <jats:tex-math>$k$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -uniform\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline6.png\"\/>\n                        <jats:tex-math>$n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -vertex hypergraph\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline7.png\"\/>\n                        <jats:tex-math>$G$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    with minimum\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline8.png\"\/>\n                        <jats:tex-math>$(k-1)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -degree\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline9.png\"\/>\n                        <jats:tex-math>$\\delta (G) \\ge (1\/2+o(1))n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    contains a tight Hamilton cycle with high discrepancy, that is, with at least\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000057_inline10.png\"\/>\n                        <jats:tex-math>$n\/r+\\Omega (n)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    edges of one colour. The minimum degree condition is asymptotically best possible and our theorem also implies a corresponding result for perfect matchings. Our tools combine various structural techniques such as Tur\u00e1n-type problems and hypergraph shadows with probabilistic techniques such as random walks and the nibble method. We also propose several intriguing problems for future research.\n                  <\/jats:p>","DOI":"10.1017\/s0963548325000057","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T03:52:56Z","timestamp":1748577176000},"page":"565-584","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["Tight Hamilton cycles with high discrepancy"],"prefix":"10.1017","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0688-8111","authenticated-orcid":false,"given":"Lior","family":"Gishboliner","sequence":"first","affiliation":[{"name":"University of Toronto"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Glock","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Passau"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0629-5431","authenticated-orcid":false,"given":"Amedeo","family":"Sgueglia","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Passau"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,5,30]]},"reference":[{"key":"S0963548325000057_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-008-2295-z"},{"key":"S0963548325000057_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759942"},{"key":"S0963548325000057_ref14","doi-asserted-by":"publisher","DOI":"10.1137\/20M1378983"},{"key":"S0963548325000057_ref2","volume-title":"Wiley-Intersci. 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(2023) Discrepancia de ciclos hamiltonianos en hipergrafos 3-uniformes, Master\u2019s thesis, Universidad de Concepci\u00f3n."},{"key":"S0963548325000057_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2022.01.003"},{"key":"S0963548325000057_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000619"},{"key":"S0963548325000057_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581274"},{"key":"S0963548325000057_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2024.06.008"},{"key":"S0963548325000057_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80045-7"},{"key":"S0963548325000057_ref7","doi-asserted-by":"publisher","DOI":"10.37236\/12145"},{"key":"S0963548325000057_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2008.10.002"},{"key":"S0963548325000057_ref20","doi-asserted-by":"crossref","unstructured":"[20] H\u00e0n, H. , Lang, R. , Marciano, J. P. , Pavez-Sign\u00e9, M. , Sanhueza-Matamala, N. , Treglown, A. and Z\u00e1rate-Guer\u00e9n, C. Colour-bias perfect matchings in hypergraphs, arXiv: https:\/\/arxiv.org\/abs\/2408.11016, 2024.","DOI":"10.1137\/24M170483X"},{"key":"S0963548325000057_ref3","doi-asserted-by":"publisher","DOI":"10.37236\/8425"},{"key":"S0963548325000057_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230010407"},{"key":"S0963548325000057_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000516"},{"key":"S0963548325000057_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/24M1637350"},{"key":"S0963548325000057_ref18","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22947"},{"key":"S0963548325000057_ref6","doi-asserted-by":"publisher","DOI":"10.37236\/10279"},{"key":"S0963548325000057_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000280"},{"key":"S0963548325000057_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.11.013"},{"key":"S0963548325000057_ref16","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.21043"},{"key":"S0963548325000057_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90074-5"},{"key":"S0963548325000057_ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0857448-8"},{"key":"S0963548325000057_ref26","unstructured":"[26] Lu, H. , Ma, J. and Xie, S. Discrepancies of perfect matchings in hypergraphs, arXiv: https:\/\/arxiv.org\/abs\/2408.06020, 2024."},{"key":"S0963548325000057_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90022-5"},{"key":"S0963548325000057_ref11","first-page":"47","article-title":"Discrepancy of trees","volume":"30","author":"Erd\u0151s","year":"1995","journal-title":"Studia Sci. Math. 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