Research draft · Partial result · 4 September 2026

Local degree conditions for the size Ramsey numbers of star forests

By tienxion

This draft proves the conjectured formula under explicit local conditions on the diagonal maxima. It builds on Ricky Cipollini’s (rickyc’s) simultaneous-tail framework and parity-dependent lower bound, using degree control in equality cases to recover additional exact values.

This is a partial result on Erdős problem #561. The general problem remains open. The additional criterion’s priority remains to be confirmed.

AI assistance was used to develop and write the draft. The coordinating human reports mathematical review. External peer review has not taken place. The PDF contains the theorem, proof, examples, and references.