An improvement on a spernerity proof of Horrocks

A Class of Lym Orders in Divisor Lattices

“…Horrocks [8,9] gave a graph-theoretical interpretation for the t = 2 conjecture and left 116 exceptional graphs in his proof. Cheng and Lih [2] carried on further with Horrocks's reduction method to reduce the number of exceptional graphs and gave a complete proof for the t = 2 conjecture. The conjecture remains open for t = 3.…”