Extremal graph theory

../

L240_seven_root_linear_band_obstruction/: The Higman–Sims graphon has a seven-root profile envelope at least 81/1000; mixing its density vector with the balanced pentagon forces slack at least 1/1200 at density 1/4 in every convex relaxation with only a linear band restriction.

---

These claims concern extremal properties of finite graphs and their limiting density descriptions. Each claim states its hypotheses, argument, evidence and verification standing.