{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:23Z","timestamp":1787323523798,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["DYNASNET 810115"],"award-info":[{"award-number":["DYNASNET 810115"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["CoSP-GA 823748"],"award-info":[{"award-number":["CoSP-GA 823748"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["19-04113"],"award-info":[{"award-number":["19-04113"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2054452"],"award-info":[{"award-number":["DMS-2054452"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>For a fixed graph $H$, what is the smallest number of colors $C$ such that there is a proper edge-coloring of the complete graph $K_n$ with $C$ colors containing no two vertex-disjoint color-isomorphic copies, or repeats, of $H$? We study this function and its generalization to more than two copies using a variety of combinatorial, probabilistic, and algebraic techniques. For example, we show that for any tree $T$ there exists a constant $c$ such that any proper edge-coloring of $K_n$ with at most $c n^2$ colors contains two repeats of $T$, while there are colorings with at most $c' n^{3\/2}$ colors for some absolute constant $c'$ containing no three repeats of any tree with at least two edges. We also show that for any graph $H$ containing a cycle there exist $k$ and $c$ such that there is a proper edge-coloring of $K_n$ with at most $c n$ colors containing no $k$ repeats of $H$, while for a tree $T$ with $m$ edges, a coloring with $o(n^{(m+1)\/m})$ colors contains $\\omega(1)$ repeats of $T$.<\/jats:p>","DOI":"10.1137\/21m1414103","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T12:12:50Z","timestamp":1632831170000},"page":"2249-2264","source":"Crossref","is-referenced-by-count":4,"title":["Repeated Patterns in Proper Colorings"],"prefix":"10.1137","volume":"35","author":[{"given":"David","family":"Conlon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mykhaylo","family":"Tyomkyn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1592-x"},{"key":"atypb2","unstructured":"N. Alon and J. H. Spencer,\n                      The Probabilistic Method\n                      , 4th ed., Wiley Ser. Discrete Math. Optim., John Wiley & Sons, Hoboken, NJ, 2016."},{"key":"atypb3","first-page":"73","volume":"7","author":"Balla I.","year":"2017","journal-title":"Mosc. J. Comb. Number Theory"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2020.103102"},{"key":"atypb5","first-page":"939","volume":"47","author":"Bukh B.","year":"2015","journal-title":"Bull. Lond. Math. Soc."},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"B. Bukh and D. Conlon,\n                      Rational exponents in extremal graph theory\n                      , J. Eur. Math. Soc. (JEMS), 20 (2018), pp. 1747-1757.","DOI":"10.4171\/jems\/798"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000012"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1112\/blms.12295"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnz088"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/18M1218881"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1017\/fms.2020.38"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579343"},{"key":"atypb14","unstructured":"P. Gao, R. Ramadurai, I. Wanless, and N. Wormald,\n                      Full Rainbow Matchings in Graphs and Hypergraphs\n                      , preprint,https:\/\/arxiv.org\/abs\/1709.02665, 2018."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20907"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2020.03.002"},{"key":"atypb18","unstructured":"T. Gustavsson,\n                      Decompositions of Large Graphs and Digraphs with High Minimum Degree\n                      , Doctoral Dissertation, Department of Mathematics, University of Stockholm, 1991."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.37236\/8262"},{"key":"atypb20","unstructured":"P. Keevash and K. Staden,\n                      Ringel's Tree Packing Conjecture in Quasirandom Graphs\n                      , preprint,https:\/\/arxiv.org\/abs\/2004.09947, 2020."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/17M1151742"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20902"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.37236\/8801"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.2307\/2372655"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1112\/plms.12245"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"R. Montgomery, A. Pokrovskiy, and B. Sudakov,\n                      Embedding rainbow trees with applications to graph labelling and decompositions\n                      , J. Eur. Math. Soc. (JEMS), 22 (2020), pp. 3101-3132.","DOI":"10.4171\/jems\/982"},{"key":"atypb27","unstructured":"R. Montgomery, A. Pokrovskiy, and B. Sudakov,\n                      A Proof of Ringel's Conjecture\n                      , preprint,https:\/\/arxiv.org\/abs\/2001.02665, 2020."},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2018.05.036"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2018.03.005"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/14220"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(75)90067-9"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1414103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:34Z","timestamp":1787321254000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1414103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/21M1414103"],"URL":"https:\/\/doi.org\/10.1137\/21m1414103","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}