{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:37Z","timestamp":1759063417146,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with different colors. It is well-known (see for example in Gy\u00e1rf\u00e1s (1980)) that in every proper coloring of a $k$-chromatic graph there is a colorful path $P_k$ on $k$ vertices. The first author proved in 1987 that $k$-chromatic and triangle-free graphs have a path $P_k$ which is an induced subgraph. N.R. Aravind conjectured that these results can be put together: in every proper coloring of a $k$-chromatic triangle-free graph, there is an induced colorful $P_k$. Here we prove the following weaker result providing some evidence towards this conjecture: For a suitable function $f(k)$, in any proper coloring of an $f(k)$-chromatic graph of girth at least five, there is an induced colorful path on $k$ vertices.<\/jats:p>","DOI":"10.37236\/6239","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:41:16Z","timestamp":1578685276000},"source":"Crossref","is-referenced-by-count":5,"title":["Induced Colorful Trees and Paths in Large Chromatic Graphs"],"prefix":"10.37236","volume":"23","author":[{"given":"Andras","family":"Gyarfas","sequence":"first","affiliation":[]},{"given":"Gabor","family":"Sarkozy","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,12,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:06:42Z","timestamp":1579237602000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,23]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6239","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,12,23]]},"article-number":"P4.46"}}