3 problems

Let $r$ be a rational number with $r\geq 2$. For a graph $G$, let $ch^s_f(G)$ denote its strong fractional choice number, and let $\chi^s_{f,P}(G)$ denote its strong fractional pai…

Let $C_5^+$ be the graph obtained from the 5-cycle $C_5$ by adding the edge indicated in the paper, and let $f(w,G)$ denote the maximum number of colors that an adversary can force…

Let $G$ be a non-edgeless multigraph, let $t\in\mathbb{N}$, and let $\chi_{\textit{OL}}^t(G)$ denote the worst-case number of rounds required for on-line scheduling when each verte…