{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:49Z","timestamp":1753893769330,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For an undirected tree with edges labeled by single letters, we consider its substrings, which are labels of the simple paths between two nodes. A palindrome is a word $w$ equal to its reverse $w^R$. We prove that the maximum number of distinct palindromic substrings in a tree of $n$ edges satisfies $\\text{pal}(n)=O(n^{1.5})$. This solves an open problem of Brlek, Lafreni\u00e8re, and Proven\u00e7al (DLT 2015), who showed that $\\text{pal}(n)=\\Omega(n^{1.5})$. Hence, we settle the tight bound of $\\Theta(n^{1.5})$ for the maximum palindromic complexity of trees. For standard strings, i.e., for trees that are simple paths, the maximum palindromic complexity is exactly $n+1$.\r\nWe also propose an $O(n^{1.5} \\log^{0.5}{n})$-time algorithm reporting all distinct palindromes and an $O(n \\log^2 n)$-time algorithm finding the longest palindrome in a tree.<\/jats:p>","DOI":"10.37236\/10842","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:43Z","timestamp":1682076883000},"source":"Crossref","is-referenced-by-count":0,"title":["Tight Bound for the Number of Distinct Palindromes in a Tree"],"prefix":"10.37236","volume":"30","author":[{"given":"Pawe\u0142","family":"Gawrychowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Kociumaka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"Rytter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Wale\u0144","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,4,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:44Z","timestamp":1682076884000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i2p10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,21]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/10842","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,4,21]]},"article-number":"P2.10"}}