7 problems

Let $C_t$ be a cycle with $t$ vertices, and let $f_{C_t}(n,n)$ denote the minimum number of independent $n$-sets in $C_t$ whose collection has a rainbow independent $n$-set. Aharon…

Let $f_{\mathcal D(k)}(n)$ denote the full-rainbow parameter for the class $\mathcal D(k)$ of graphs with maximum degree at most $k$, and let $q$ be the quantity used in the source…

Let $\mathcal D(k)$ be the class of graphs whose vertex degrees are at most $k$. Bounded-degree partial rainbow conjecture. For $m\le n$, … This is presented as a generalization of…

Let $\mathcal D(k)$ be the class of graphs whose vertex degrees are at most $k$. Bounded-degree conjecture. … The source gives a general upper bound from graph colouring and says t…

Let $f_G(n,m)$ denote the least number of independent $n$-sets in a graph $G$ that guarantees a rainbow independent set of size $m$. Maximum-degree-two conjecture. If $G$ has maxim…

Let $f_G(n,m)$ denote the least number of independent $n$-sets in a graph $G$ that guarantees a rainbow independent set of size $m$. Exceptional-line-graph conjecture. If $G$ is th…

Let $C_t$ be the cycle on $t$ vertices, and let $f_{C_t}(s,s)$ denote the least number of independent sets of size $s$ in $C_t$ that guarantees a rainbow independent set of size…