{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T20:30:42Z","timestamp":1768336242553,"version":"3.49.0"},"reference-count":28,"publisher":"MathDoc\/Centre Mersenne","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>\n                    A\n                    <jats:italic>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                        <mml:mi>k<\/mml:mi>\n                      <\/mml:math>\n                      -uniform tight cycle\n                    <\/jats:italic>\n                    is a\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    -graph with a cyclic order of its vertices such that every\u00a0\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    consecutive vertices from an edge. We show that for\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:mi>k<\/mml:mi>\n                        <mml:mo>\u2265<\/mml:mo>\n                        <mml:mn>3<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    , every red-blue edge-coloured complete\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    -graph on\u00a0\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>n<\/mml:mi>\n                    <\/mml:math>\n                    vertices contains\u00a0\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    vertex-disjoint monochromatic tight cycles that together cover\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:mi>n<\/mml:mi>\n                        <mml:mo>-<\/mml:mo>\n                        <mml:mi>o<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>n<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    vertices.\n                  <\/jats:p>","DOI":"10.5802\/igt.1","type":"journal-article","created":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T08:14:00Z","timestamp":1727424840000},"page":"1-19","source":"Crossref","is-referenced-by-count":1,"title":["Almost partitioning every\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:math>\n                    -edge-coloured complete\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    -graph into\u00a0\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:math>\n                    monochromatic tight cycles"],"prefix":"10.5802","volume":"1","author":[{"given":"Allan","family":"Lo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Pfenninger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"3842","published-online":{"date-parts":[[2024,9,27]]},"reference":[{"key":"key2025101311040021230_1","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.jcta.2017.01.003","article-title":"Tight cycles and regular slices in dense hypergraphs","volume":"149","author":"Allen, Peter","year":"2017","unstructured":"[1] Allen, Peter; B\u00f6ttcher, Julia; Cooley, Oliver; Mycroft, Richard Tight cycles and regular slices in dense hypergraphs, J. 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Partitioning 2-edge-colored graphs by monochromatic paths and cycles, Combinatorica, Volume 34 (2014) no. 5, pp. 507-526","journal-title":"Combinatorica"},{"issue":"2","key":"key2025101311040021230_5","doi-asserted-by":"publisher","first-page":"1460","DOI":"10.1137\/19M1269786","article-title":"Partitioning edge-colored hypergraphs into few monochromatic tight cycles","volume":"34","author":"Bustamante, Sebasti\u00e1n","year":"2020","unstructured":"[5] Bustamante, Sebasti\u00e1n; Corsten, Jan; Frankl, N\u00f3ra; Pokrovskiy, Alexey; Skokan, Jozef Partitioning edge-colored hypergraphs into few monochromatic tight cycles, SIAM J. Discrete Math., Volume 34 (2020) no. 2, pp. 1460-1471","journal-title":"SIAM J. Discrete Math."},{"issue":"1","key":"key2025101311040021230_6","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1002\/jgt.22417","article-title":"Almost partitioning 2-colored complete 3-uniform hypergraphs into two monochromatic tight or loose cycles","volume":"91","author":"Bustamante, Sebasti\u00e1n","year":"2019","unstructured":"[6] Bustamante, Sebasti\u00e1n; H\u00e0n, Hi\u1ec7p; Stein, Maya Almost partitioning 2-colored complete 3-uniform hypergraphs into two monochromatic tight or loose cycles, J. Graph Theory, Volume 91 (2019) no. 1, pp. 5-15","journal-title":"J. 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Combin."},{"issue":"7","key":"key2025101311040021230_17","doi-asserted-by":"publisher","first-page":"1970","DOI":"10.1016\/j.disc.2015.07.007","article-title":"Vertex covers by monochromatic pieces\u2014a survey of results and problems","volume":"339","author":"Gy\u00e1rf\u00e1s, Andr\u00e1s","year":"2016","unstructured":"[17] Gy\u00e1rf\u00e1s, Andr\u00e1s Vertex covers by monochromatic pieces\u2014a survey of results and problems, Discrete Math., Volume 339 (2016) no. 7, pp. 1970-1977","journal-title":"Discrete Math."},{"issue":"1","key":"key2025101311040021230_18","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1002\/jgt.3190070116","article-title":"Vertex coverings by monochromatic paths and cycles","volume":"7","author":"Gy\u00e1rf\u00e1s, Andr\u00e1s","year":"1983","unstructured":"[18] Gy\u00e1rf\u00e1s, Andr\u00e1s Vertex coverings by monochromatic paths and cycles, J. Graph Theory, Volume 7 (1983) no. 1, pp. 131-135","journal-title":"J. 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B"},{"issue":"1","key":"key2025101311040021230_20","doi-asserted-by":"publisher","DOI":"10.37236\/7239","article-title":"Monochromatic cycle partitions of 2-coloured graphs with minimum degree <span class=\"mathjax-formula\" data-tex=\"$3n\/4$\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mn>3<\/mn><mi>n<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><\/math><\/span>","volume":"26","author":"Letzter, Shoham","year":"2019","unstructured":"[20] Letzter, Shoham Monochromatic cycle partitions of 2-coloured graphs with minimum degree 3n\/4, Electron. J. Combin., Volume 26 (2019) no. 1, P1.19, 67 pages","journal-title":"Electron. J. Combin."},{"issue":"1","key":"key2025101311040021230_21","doi-asserted-by":"publisher","DOI":"10.37236\/10604","article-title":"Towards Lehel\u2019s conjecture for 4-uniform tight cycles","volume":"30","author":"Lo, Allan","year":"2023","unstructured":"[21] Lo, Allan; Pfenninger, Vincent Towards Lehel\u2019s conjecture for 4-uniform tight cycles, Electron. J. Combin., Volume 30 (2023) no. 1, P1.13, 36 pages","journal-title":"Electron. J. Combin."},{"key":"key2025101311040021230_22","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.jctb.2014.01.003","article-title":"Partitioning edge-coloured complete graphs into monochromatic cycles and paths","volume":"106","author":"Pokrovskiy, Alexey","year":"2014","unstructured":"[22] Pokrovskiy, Alexey Partitioning edge-coloured complete graphs into monochromatic cycles and paths, J. Combin. Theory Ser. B, Volume 106 (2014), pp. 70-97","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"key2025101311040021230_23","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2022.113161","article-title":"Partitioning a graph into a cycle and a sparse graph","volume":"346","author":"Pokrovskiy, Alexey","year":"2023","unstructured":"[23] Pokrovskiy, Alexey Partitioning a graph into a cycle and a sparse graph, Discrete Math., Volume 346 (2023) no. 1, 113161, 21 pages","journal-title":"Discrete Math."},{"key":"key2025101311040021230_24","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/978-3-662-59204-5_14","article-title":"Embedding graphs into larger graphs: results, methods, and problems","volume":"28","author":"Simonovits, Mikl\u00f3s","year":"2019","unstructured":"[24] Simonovits, Mikl\u00f3s; Szemer\u00e9di, Endre Embedding graphs into larger graphs: results, methods, and problems, Building bridges II\u2014mathematics of L\u00e1szl\u00f3 Lov\u00e1sz (Bolyai Soc. Math. Stud.), Volume 28, Springer, Berlin, 2019, pp. 445-592","journal-title":"Building bridges II\u2014mathematics of L\u00e1szl\u00f3 Lov\u00e1sz"},{"key":"key2025101311040021230_25","doi-asserted-by":"publisher","DOI":"10.37236\/11465","article-title":"Monochromatic paths in 2-edge-coloured graphs and hypergraphs","volume":"30","author":"Stein, Maya","year":"2023","unstructured":"[25] Stein, Maya Monochromatic paths in 2-edge-coloured graphs and hypergraphs, Electron. J. Combin., Volume 30 (2023), P1.53, 12 pages","journal-title":"Electron. J. Combin."},{"key":"key2025101311040021230_26","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.disc.2014.06.025","article-title":"Improved monochromatic loose cycle partitions in hypergraphs","volume":"334","author":"S\u00e1rk\u00f6zy, G\u00e1bor N.","year":"2014","unstructured":"[26] S\u00e1rk\u00f6zy, G\u00e1bor N. Improved monochromatic loose cycle partitions in hypergraphs, Discrete Math., Volume 334 (2014), pp. 52-62","journal-title":"Discrete Math."},{"issue":"4","key":"key2025101311040021230_27","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1017\/S0963548398003599","article-title":"Partitioning two-coloured complete graphs into two monochromatic cycles","volume":"7","author":"\u0141uczak, Tomasz","year":"1998","unstructured":"[27] \u0141uczak, Tomasz; R\u00f6dl, Vojt\u011bch; Szemer\u00e9di, Endre Partitioning two-coloured complete graphs into two monochromatic cycles, Combin. Probab. Comput., Volume 7 (1998) no. 4, pp. 423-436","journal-title":"Combin. Probab. Comput."},{"issue":"2","key":"key2025101311040021230_28","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1006\/jctb.1998.1874","article-title":"<span class=\"mathjax-formula\" data-tex=\"${R}({C}_n,{C}_n,{C}_n)\\le (4+o(1))n$\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi>R<\/mi><mrow><mo>(<\/mo><msub><mi>C<\/mi> <mi>n<\/mi> <\/msub><mo>,<\/mo><msub><mi>C<\/mi> <mi>n<\/mi> <\/msub><mo>,<\/mo><msub><mi>C<\/mi> <mi>n<\/mi> <\/msub><mo>)<\/mo><\/mrow><mo>\u2264<\/mo><mrow><mo>(<\/mo><mn>4<\/mn><mo>+<\/mo><mi>o<\/mi><mrow><mo>(<\/mo><mn>1<\/mn><mo>)<\/mo><\/mrow><mo>)<\/mo><\/mrow><mi>n<\/mi><\/mrow><\/math><\/span>","volume":"75","author":"\u0141uczak, Tomasz","year":"1999","unstructured":"[28] \u0141uczak, Tomasz R(C n ,C n ,C n )\u2264(4+o(1))n, J. Combin. Theory Ser. B, Volume 75 (1999) no. 2, pp. 174-187","journal-title":"J. Combin. Theory Ser. B"}],"container-title":["Innovations in Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/igt.centre-mersenne.org\/item\/10.5802\/igt.1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T09:04:23Z","timestamp":1760346263000},"score":1,"resource":{"primary":{"URL":"https:\/\/igt.centre-mersenne.org\/articles\/10.5802\/igt.1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,27]]},"references-count":28,"alternative-id":["10.5802\/igt.1"],"URL":"https:\/\/doi.org\/10.5802\/igt.1","relation":{},"ISSN":["3050-743X"],"issn-type":[{"value":"3050-743X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,27]]}}}