11 problems

The sharp alpha-metric hyperbolicity conjecture. The right upper bound for the hyperbolicity of an $\alpha_i$-metric graph might be

A graph $G$ is $(\lambda,\mu)$-bow metric if, whenever shortest paths $P(u,w)$ and $P(v,x)$ share a common shortest subpath $P(v,w)$ of length more than $\lambda$, one has … A grap…

The cycle–quadruple conjecture. The following statements are equivalent: if $H$ is the induced subgraph of $G$ with vertex set $X$, then $H$ is a cycle; and the points of $X$ can b…

Let $G$ be a nonempty connected graph. Write $V(G)$ for its vertex set and $d_G$ for its geodesic distance. Let $\mathfrak{MB}$ denote the class of metric spaces $(X,d)$ such that…

For graphs equipped with the distance $d_{GLG}$ induced by the Euclidean distance between their Game of Life on Graphs feature vectors, consider triples satisfying … The topologica…

Let $G$ be a distance-regular graph of diameter $d$ with eigenvalues $\theta_0>\theta_1>\cdots>\theta_d$. For the cosine sequence…

Let $G$ be a distance-regular graph with diameter $d$, with eigenvalues $\theta_0>\theta_1>\cdots>\theta_d$ and cosine sequences $(w_0(\theta_j),\ldots,w_d(\theta_j))$ correspondin…

Let $G$) be a distance-regular graph with diameter $d$, valency $k$, eigenvalues $\theta_0>\theta_1>ots>\theta_d$, and standard sequences $(w_0(\theta_j),...,w_d(\theta_j))$ corres…

Affine preferential attachment metric conjecture. The function $d_\delta$ is a metric on trees with at least $3$ vertices.

Bubeck–Mossel–Rácz metric conjecture. The function $d$ is a metric in non-trivial cases.

Triangle-free relaxed-minor conjecture. If $H$ is triangle-free, then every relaxed-minor model of $H$ in $G$ can be converted into a minor model of $H$ in $G$; equivalently, the n…