 Minimum-degree Ramsey lower bound

For a finite simple graph $H$ of minimum degree of a graph $d$, its ordinary two-colour graph Ramsey number satisfiesThe lower bound also applies when $H$ contains a subgraph of minimum degree at least $d$, since a monochromatic copy of $H$ would contain a monochromatic copy of that subgraph. The paragraph before Corollary1.7 of Ordered Ramsey numbers by David Conlon and others records this ordinary Ramsey bound before comparing it with ordered Ramsey numbers.^[ref]

For $H=K_t$, this gives $R(K_t)\ge 2^{(t-1)/2}$. Thus even without using the entire degree sequence, a large minimum degree already forces an exponential obstruction to guaranteeing a monochromatic copy.