Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery

ArXi:2604.21187v1 Announce Type: cross Ramsey-good graphs are graphs that contain neither a clique of size $s$ nor an independent set of size $t$. We study doubly saturated Ramsey-good graphs, defined as Ramsey-good graphs in which the addition or removal of any edge necessarily creates an $s$-clique or a $t$-independent set. We present a method combining SAT solving with bespoke LLM-generated code to discover infinite families of such graphs, answering a question of Grinstead and Roberts from 1982. In addition, we use LLMs to generate and formalize correctness proofs in Lean.