1 research outputs found
Tight Bound for the Number of Distinct Palindromes in a Tree
For an undirected tree with edges labelled by single letters, we consider
its substrings, which are labels of the simple paths between pairs of nodes. We
prove that there are different palindromic substrings. This solves
an open problem of Brlek, Lafreni\`ere, and Proven\c{c}al (DLT 2015), who gave
a matching lower-bound construction. Hence, we settle the tight bound of
for the maximum palindromic complexity of trees. For standard
strings, i.e., for paths, the palindromic complexity is . We also propose
-time algorithm for reporting all distinct palindromes in
an undirected tree with edges