{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T13:00:12Z","timestamp":1773406812736,"version":"3.50.1"},"reference-count":36,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Committee for Scientific Research","award":["1P03A 017 27"],"award-info":[{"award-number":["1P03A 017 27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>A vertex coloring<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E1\"><mml:mi>f<\/mml:mi><\/mml:math>of a graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E2\"><mml:mi>G<\/mml:mi><\/mml:math>is<jats:italic>nonrepetitive<\/jats:italic>if there are no integer<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E3\"><mml:mrow><mml:mi>r<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:math>and a simple path<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E4\"><mml:mrow><mml:msub><mml:mi>v<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mi>v<\/mml:mi><mml:mrow><mml:mn>2<\/mml:mn><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E5\"><mml:mi>G<\/mml:mi><\/mml:math>such that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E6\"><mml:mrow><mml:mi>f<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:msub><mml:mi>v<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:msub><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>f<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:msub><mml:mi>v<\/mml:mi><mml:mrow><mml:mi>r<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>i<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>for all<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E7\"><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:math>. This notion is a graph-theoretic variant of nonrepetitive sequences of Thue. The paper surveys problems and results on this topic.<\/jats:p>","DOI":"10.1155\/2007\/74639","type":"journal-article","created":{"date-parts":[[2007,2,5]],"date-time":"2007-02-05T09:39:57Z","timestamp":1170668397000},"page":"1-10","source":"Crossref","is-referenced-by-count":21,"title":["Nonrepetitive Colorings of Graphs\u0097A Survey"],"prefix":"10.1155","volume":"2007","author":[{"given":"Jaroslaw","family":"Grytczuk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","first-page":"1","volume":"7","year":"1906","journal-title":"Norske Videnskabers Selskabs Skrifter, I Mathematisch-Naturwissenschaftliche Klasse, Christiania"},{"key":"2","first-page":"xvi+571","year":"2003"},{"key":"3","series-title":"Publications du LaCIM","volume":"20","year":"1995"},{"key":"4","series-title":"Publications du LaCIM","first-page":"65","volume-title":"Axel Thue's work on repetitions in words","year":"1992"},{"key":"5","series-title":"Encyclopedia of Mathematics and Its Applications","first-page":"xix+238","volume":"17","year":"1983"},{"key":"6","series-title":"Encyclopedia of Mathematics and Its Applications","first-page":"xiv+504","volume":"90","year":"2002"},{"key":"7","first-page":"195","volume":"321","year":"1981","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"8","first-page":"1","volume":"327","year":"1981","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"9","first-page":"44","volume":"330","year":"1982","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"10","series-title":"Wiley-Interscience Series in Discrete Mathematics and Optimization","first-page":"xviii+301","year":"2000"},{"key":"11","series-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai","first-page":"103","volume-title":"An application of Lov\u00e1sz local lemma: there exists an infinite 01-sequence containing no near identical intervals","volume":"37","year":"1984"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.01.004"},{"issue":"1, r44","key":"13","first-page":"1","volume":"9","year":"2002","journal-title":"Electronic Journal of Combinatorics"},{"issue":"1, n10","key":"14","first-page":"1","volume":"9","year":"2002","journal-title":"Electronic Journal of Combinatorics"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10057"},{"key":"16"},{"key":"17"},{"key":"18","first-page":"209","volume-title":"Nonrepetitive graph coloring","year":"2006"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1023\/B:ORDE.0000026489.93166.cb"},{"issue":"6","key":"20","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1016\/j.ejc.2005.01.010","volume":"27","year":"2006","journal-title":"European Journal of Combinatorics"},{"key":"21"},{"issue":"2","key":"22","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.disc.2006.06.017","volume":"307","year":"2007","journal-title":"Discrete Mathematics"},{"key":"23","first-page":"1","volume":"1","year":"1912","journal-title":"Norske Videnskabers Selskabs Skrifter, I Mathematisch-Naturwissenschaftliche Klasse, Christiania"},{"key":"24","series-title":"Lecture Notes in Comput. 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