27 problems

Let $\mathcal{M}$ be the family of complete multipartite graphs, and let $I_H(x)$ denote the inducibility profile of a graph $H$. Unbounded-local-maxima conjecture. For every $k>0$…

The conjectured profile of $K_{2,2,1}$. The function is conjectured to satisfy

Let $S_{2,1}$ be the relevant colored graph, and let an $S_{2,1}$-good sequence $(G_n)$ have limiting edge density $\beta$ and profile $\rho(S_{2,1},(G_n))$. Define the constructio…

Edge inducibility conjecture for odd paths. If $k\geq 5$ is odd, then

Let $d$ and $i$ be positive integers with $1\leq i<d$. Define … Let $i(K_{i,d-i})$ denote the inducibility of the complete bipartite graph $K_{i,d-i}$. E(d,i) density conjecture. E…

Let $H$ be a configuration in $Q_d$, and let $\lambda(H,d)$ denote its $d$-cube density. Classification conjecture above $5/8$. If … then either $H$ is layered and…

Let $W_7,W_8,W_9,W_{10}$, and $W_{12}$ be the configurations in $Q_3$ listed in Table, and let their lower bounds there be the corresponding values of their 3-cube densities. The e…

Let $C_k$ denote the cycle graph on $k$ vertices, and let $\mathcal{I}(C_k)$ be its inducibility, the limiting maximum proportion of induced copies of $C_k$ in graphs with an incre…

Let $C_k$ be the $k$-vertex carousel tournament, and let $C_n$ be the carousel tournament on $n$ vertices. For a tournament $T$, write $I(C_k,T)$ for the number of induced copies o…

Transitive-tournament-free inducibility conjecture. The number of induced copies of $\vec{P}_k$ over all $\vec{T}_3$-free oriented graphs on $n$ vertices is maximized by a balanced…

Iterated blow-up conjecture. The number of induced copies of $\vec{P}_k$ over all oriented graphs on $n$ vertices is maximized by an iterated balanced blow-up of $\vec{C}_{k+1}$. C…

Quadratic-range edge-statistics conjecture. For all $k,\ell\in\mathbb{N}$ with

Sparse-edge decay conjecture. For all $k,\ell\in\mathbb{N}$ with

Edge-statistics conjecture. For all $k,\ell\in\mathbb{N}$ with $0<\ell<\binom{k}{2}$, we have

Hypergraph logarithm-free inducibility bound conjecture. For any $r,k$ and any $0\le\ell\le\binom{k}{r}$, we have

Logarithm-free inducibility bound conjecture. For all $k$ and all $0\le\ell\le\binom{k}{2}$, we have

Alon–Hefetz–Krivelevich–Tyomkyn's superlinear sparsity conjecture. For all $k,\ell$ satisfying

Alon–Hefetz–Krivelevich–Tyomkyn's 1/e conjecture. For all $0<\ell<\binom{k}{2}$ we have

Let $\operatorname{ind}(k,\ell)$ denote the limiting maximum proportion of $k$-vertex subsets inducing exactly $\ell$ edges. Quadratic edge-statistics conjecture. For all pairs…

Let $\operatorname{ind}(k,\ell)$ denote the limiting maximum proportion of $k$-vertex subsets inducing exactly $\ell$ edges. Super-linear edge-statistics conjecture. For all pairs…

For a finite graph $H$, let $\operatorname{ind}(H)$ denote its inducibility, and let $K_{|H|}$ and $\overline{K}_{|H|}$ be respectively the complete and edgeless graphs on $|H|$ ve…

Let $H$ be a strongly asymmetric graph on $h$ vertices. Let $i_H(n)$ be the maximum number of induced copies of $H$ in an $n$-vertex graph, and let $g(n,h)$ be the recursively defi…

Let $\operatorname{E}_n$ denote the rooted binary tree with $n$ leaves, and let $c(F,T)$ be the number of copies of a rooted binary tree $F$ in a rooted binary tree $T$. For intege…

Let $\vec{S}_k$ be the directed star on $k$ vertices, with one center and $k-1$ edges oriented away from it. For an integer $k\geq 3$, let $\pi_{\vec{S}_k}(\emptyset)$ denote the m…

The directed out-star conjecture. For every $k\geq3$,