7 problems

Let $Q_n$ be the $n$-dimensional hypercube, and let $W(Q_n)$ denote the maximum number of colors in an interval coloring of $Q_n$. Petrosyan's conjecture. … for any…

Let $G$ be an outerplanar graph. Its interval coloring impropriety is the least integer $k$ for which $G$ has a $k$-improper interval edge coloring, and is denoted by…

Let $\mathfrak{N}_c$ be the class of multigraphs admitting a cyclic interval coloring, and let $W_c(G)$ denote the maximum number of colors in a cyclic interval coloring of $G$. Pe…

Let $K_{2n}$ be the complete graph on $2n$ vertices, and let $W(K_{2n})$ be the greatest number of colors in an interval coloring of $K_{2n}$. Write $\left\|n_2\right\|$ for the nu…

Let $G$ be a connected graph with at least two vertices, let $V(G)$ be its vertex set, and let $\mathfrak{N}_{c}$ denote the class of interval cyclically colorable graphs. Write…

Let $K_{k,m,n}$ be the complete tripartite graph with part sizes $k,m,n$, where $k\leq m\leq n$ and $n>k+m$. Reduction conjecture. … This is proposed as a generalization of the…

Let $K_{1,m,n}$ be the complete tripartite graph with part sizes $1,m,n$, and let an interval $t$-coloring mean an interval edge-coloring using the colors $1,\ldots,t$. Exact-spect…