  We study the universal character ring of some families of one-relator groups.
As an application, we calculate the universal character ring of two-generator
one-relator groups whose relators are palindrome, and, in particular, of the
(-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the
(-2,3,2n+1)-pretzel knot, we give a less technical proof of a result in [LT1]
on its universal character ring, and an elementary proof of a result in [Ma] on
the number of irreducible components of its character variety.
