6 problems

Cornet–Dravec–Torres conjecture. For every odd integer $n\ge 7$,

Lexicode conjecture. Assume that $k>1$ is a power of $2$. The lexicode $$ has cardinality

Let $F_k(K_n)$ be the $k$-token graph of the complete graph $K_n$, and let $\operatorname{pw}$ and $\operatorname{tw}$ denote pathwidth and treewidth. Optimal path-decomposition co…

For integers $n$ and $k$ with $1\le k\le n-1$, let $F_k(K_n)$ be the $k$-token graph of the complete graph $K_n$, also known as the Johnson graph. The tree decomposition of this gr…

Let $G_n=K(n,2)$ be the Johnson graph whose vertices are the $2$-subsets of an $n$-element set, with two vertices adjacent when the corresponding subsets intersect in one element.…

Karloff's conjecture. If $n=2d$ and $j>d/2$, then the smallest eigenvalue of $J(n,d,j)$ is $E_j(1)$. The surrounding text says that this conjecture is settled in the paper, so the…