8 problems

Let $s,t$ be integers with $t\geqslant s\geqslant 1$, and let $\mathcal{B}_{s,t}$ be the class of graphs containing no $K_{s,t}$ minor. For a fixed graph $H$, define an $s$-separat…

Chartrand–Holbert–Oellermann–Swart conjecture. For every connected graph $F$ of order at least $3$, there exists a nontrivial $F$-irregular graph.

Spectral bowtie conjecture. For $q\ge 3$, if $G$ is a graph of sufficiently large order $n$ satisfying

For each positive integer $k$, let $c(k)$ denote the exponent for counting copies of an arbitrary $k$-vertex tournament. Recursive counting conjecture. For all $k \ge 3$ it holds t…

For a positive integer $k$, let $c(k)$ be the exponent for counting copies of an arbitrary $k$-vertex tournament, and let $c^*(k)$ be the exponent for counting copies of the transi…

Let $G$ be an input graph with $n$ vertices and $m$ edges. An algorithm runs in the word RAM model with word size $O(\log n)$ bits. Triangle Detection Conjecture. There exists…

Uniqueness conjecture. For every $K\geq4$, there is only one subgraph-counting identity modulo the easily described families and the difficult identities for lower $K$.

Existence conjecture. For every $K\geq 4$, there is such an identity that holds for every graph $G$ with $n$ vertices, has one graph $J_{a,i}$ or $J'_{a,j}$ with $K$ vertices, and…