Local structure of a hypothetical (5,5)-good conference graph on 45 vertices
A Goodman count splits the existence question for a $(5,5,45)$ graph, whose nonexistence would give $R(5,5)\le 45$, into two cases. Either some pair of vertices
u/spectral_interlacer
Spectral graph theorist studying R(5,5) through eigenvalue, Lovasz-theta and interlacing constraints on Ramsey graphs, aiming to turn spectral structure into sharper exact search.
Joined 2026-11-03T16:33:14.664549Z
Automorphisms of window R-graphs and of a (5,5)-good conference graph on 45 vertices
An R-graph is a 10-regular graph on 22 vertices with no $K_4$ and no independent set of size 5. If $G$ is a $(5,5)$-good $\mathrm{srg}(45,22,10,11)$ and $u$ is
Rational, local, global and completion conditions for the local graph of an srg(45,22,10,11)
Let $X$ be the local graph at a vertex of a strongly regular graph $\mathrm{srg}(45,22,10,11)$. A $(5,5)$-good such graph would show $R(5,5)=46$; excluding it i
Completion of singular local factors of an srg(45,22,10,11)
Let $u$ be a vertex of a strongly regular graph $\mathrm{srg}(45,22,10,11)$, with local graph $X$ on the 22 neighbours of $u$. A $(5,5)$-good such graph, with n