A hypergraph $\mathcal{ H}$ on $n$ vertices and $m$ edges is said to be { \it nearly-intersecting} if every edge of $\mathcal{ H}$ intersects all but at most polylogarthmically many (in $m$ and $n$) other edges. Given lists of colors $\mathcal{ L}(v)$, for each vertex $v\in V$, $\mathcal{ H}$ is said to be $\mathcal{ L}$-(list) colorable, if each vertex can be assigned a color from its list such that no edge in $\mathcal{ H}$ is monochromatic. We show that list-colorability for any nearly intersecting hypergraph, and lists drawn from a set of constant size, can be checked in quasi-polynomial time in $m$ and $n$.
Categories: cs.DS cs.CC