{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T21:06:26Z","timestamp":1761599186192,"version":"build-2065373602"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T00:00:00Z","timestamp":1758758400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T00:00:00Z","timestamp":1758758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008332","name":"Graz University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008332","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A\n                    <jats:italic>k<\/jats:italic>\n                    -\n                    <jats:italic>uniform tight cycle<\/jats:italic>\n                    is a\n                    <jats:italic>k<\/jats:italic>\n                    -graph with a cyclic ordering of its vertices such that its edges are precisely the sets of\u00a0\n                    <jats:italic>k<\/jats:italic>\n                    consecutive vertices in that ordering. We show that, for each\n                    <jats:inline-formula>\n                      <jats:tex-math>$$k \\ge 3$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , the Ramsey number of the\n                    <jats:italic>k<\/jats:italic>\n                    -uniform tight cycle on\n                    <jats:italic>kn<\/jats:italic>\n                    vertices is\n                    <jats:inline-formula>\n                      <jats:tex-math>$$(1+o(1))(k+1)n$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . This is an extension to all uniformities of previous results for\n                    <jats:inline-formula>\n                      <jats:tex-math>$$k = 3$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    by Haxell, \u0141uczak, Peng, R\u00f6dl, Ruci\u0144ski, and Skokan and for\n                    <jats:inline-formula>\n                      <jats:tex-math>$$k = 4$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    by Lo and the author and confirms a special case of a conjecture by the former set of authors. Lehel\u2019s conjecture, which was proved by Bessy and Thomass\u00e9, states that every red-blue edge-coloured complete graph contains a red cycle and a blue cycle that are vertex-disjoint and together cover all the vertices. We also prove an approximate version of this for\n                    <jats:italic>k<\/jats:italic>\n                    -uniform tight cycles. We show that, for every\n                    <jats:inline-formula>\n                      <jats:tex-math>$$k \\ge 3$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , every red-blue edge-coloured complete\n                    <jats:italic>k<\/jats:italic>\n                    -graph on\n                    <jats:italic>n<\/jats:italic>\n                    vertices contains a red tight cycle and a blue tight cycle that are vertex-disjoint and together cover\n                    <jats:inline-formula>\n                      <jats:tex-math>$$n - o(n)$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    vertices.\n                  <\/jats:p>","DOI":"10.1007\/s00493-025-00173-z","type":"journal-article","created":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T10:37:25Z","timestamp":1758796645000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On k-uniform Tight Cycles: the Ramsey Number for $$C_{kn}^{(k)}$$ and an Approximate Lehel\u2019s Conjecture"],"prefix":"10.1007","volume":"45","author":[{"given":"Vincent","family":"Pfenninger","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,25]]},"reference":[{"issue":"4","key":"173_CR1","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1017\/S0963548308009164","volume":"17","author":"P Allen","year":"2008","unstructured":"Allen, P.: Covering two-edge-coloured complete graphs with two disjoint monochromatic cycles. Combin. Probab. Comput. 17(4), 471\u2013486 (2008)","journal-title":"Combin. Probab. Comput."},{"issue":"2","key":"173_CR2","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/j.jctb.2009.07.001","volume":"100","author":"S Bessy","year":"2010","unstructured":"Bessy, S., Thomass\u00e9, S.: Partitioning a graph into a cycle and an anticycle, a proof of lehel\u2019s conjecture. J. Combin. Theory Ser. B 100(2), 176\u2013180 (2010)","journal-title":"J. Combin. Theory Ser. B"},{"key":"173_CR3","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/S0095-8956(73)80005-X","volume":"14","author":"JA Bondy","year":"1973","unstructured":"Bondy, J.A., Erd\u0151s, P.: Ramsey numbers for cycles in graphs. J. Combin. Theory Ser. B 14, 46\u201354 (1973)","journal-title":"J. Combin. Theory Ser. 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In preparation"},{"key":"173_CR7","unstructured":"Haxell, P.\u00a0E., \u0141uczak, T., Peng,Y., R\u00f6dl,V., Ruci\u0144ski, A., Skokan, J.: The Ramsey number for hypergraph cycles II. CDAM Research Report, LSE-CDAM-2007-04,( 2007)"},{"issue":"1\u20132","key":"173_CR8","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1017\/S096354830800967X","volume":"18","author":"PE Haxell","year":"2009","unstructured":"Haxell, P.E., \u0141uczak, T., Peng, Y., R\u00f6dl, V., Ruci\u0144ski, A., Skokan, J.: The Ramsey number for 3-uniform tight hypergraph cycles. Combin. Probab. Comput. 18(1\u20132), 165\u2013203 (2009)","journal-title":"Combin. Probab. Comput."},{"issue":"1","key":"173_CR9","doi-asserted-by":"publisher","first-page":"1.13","DOI":"10.37236\/10604","volume":"30","author":"A Lo","year":"2023","unstructured":"Lo, A., Pfenninger, V.: Towards Lehel\u2019s conjecture for 4-uniform tight cycles. Electron. J. Combin. 30(1), 1.13-36 (2023)","journal-title":"Electron. J. 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