3 problems

Let $G$ be a simple graph with even degrees $d_1,\ldots,d_n$. Let $\operatorname{EO}(G)$ denote the number of Eulerian orientations of $G$, and let $\operatorname{RT}(d+1)$ denote…

Let $G=G(n)$ be a sequence of simple graphs with even degree sequence $\boldsymbol{d}=\boldsymbol{d}(n)$. Write $d_{\mathrm{hm}}$ for the harmonic mean degree, and let $\rho(G)$ de…

Let $t$ be the generating-function variable, let $k$ be the approximation parameter, and let $\bar\mu_k$ denote the estimated growth rate associated with the algebraic generating s…