In the November Colloquy, Sir Jeremy Morse postulated that TAPERINGLY is the longest heterogram having no alphabetically-adjacent letters. By this he meant no two letters in the word are adjacent in the alphabet--for example, if the word has an O in it, it cannot have an N or P. However, I at first interpreted it to mean no bigrams of the form AB,BC, ... YZ, as much weaker restriction. So here are two puzzles for the price of one!
"Heterograms With No Adjacent Letters,"
Word Ways: Vol. 32
, Article 18.
Available at: https://digitalcommons.butler.edu/wordways/vol32/iss1/18