Palindromic width of graph of groups

Abstract

In this paper, we answer questions raised by Bardakov and Gongopadhyay (Commun. Algebra43(11) (2015) 4809–4824). We prove that the palindromic width of HNN extension of a group by proper associated subgroups is infinite. We also prove that the palindromic width of the amalgamated free product of two groups via a proper subgroup is infinite (except when the amalgamated subgroup has index two in each of the factors). Combining these results it follows that the palindromic width of the fundamental group of a graph of groups is mostly infinite.