5 problems

Let $G$ be a graph with chromatic number $k$, let $G^r$ denote its $r$-uniform power, and let $m'(G)$ be the number of edges between a specified pair of color classes of a $(k-1)$-…

Let $F$ be a graph, let $\rchi(F)$ denote its chromatic number, let $q(F)$ be the minimum number of red vertices in a strong red-blue coloring of $F$, and let $H_i$ be the 3-unifor…

General formula in terms of $Z(d)$.

Intermediate-value conjecture. For $7\leq d<i<Z(d)$,

General formula conjecture. The formula given in Theorem 1 is valid for all natural numbers $d$ and $m$, with no condition on $d$ and $m$.