2 problems

For a degree sequence $\mathbf{d}=\{d_1,d_2,\ldots,d_n\}$, let $m=(\sum d_i)/2$ be the number of edges in any realization, and let … For realizations $G_1$ and $G_2$ of this degree…

Let $G$ be a balanced red-blue graph with $n$ vertices and $m$ edges. An alternating-circuit bound asserts that 1. there exists an alternating circuit of length at most $3n^2/m$; a…