8 problems

Let $\mathbf{d}$ be a graphical degree sequence that is not potentially bipartite, and let $k\ge 3$ be fixed. A realization of $\mathbf{d}$ is a simple graph with degree sequence…

Let a degree sequence be power-law distribution-bounded with exponent $\gamma$ when it belongs to the power-law distribution-bounded class described in the source. Gao–Wormald's co…

Let a switch Markov chain be the chain on realizations of a degree sequence that performs a switch, for an unconstrained, bipartite, or directed degree sequence. A degree sequence…

Monotonicity conjecture. The ratio $D_f(n)/D(n)$ is monotonously increasing when $n\geq 8$.

Prevalence conjecture.

Algorithmic conjecture. Algorithm $$ runs in time polynomial in $n$ on average.

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…