Quasi-polynomial algorithms for list-coloring of nearly intersecting hypergraphs

A hypergraph 7-t on n vertices and m edges is said to be nearly-intersecting if every edge of 7-t intersects all but at most polylogarthmically many (in m and n) other edges. Given lists of colors G(v), for each vertex v is an element of V, 7-t is said to be G-(list) colorable, if each vertex can be assigned a color from its list such that no edge in 7-t 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. (c) 2021 Elsevier B.V. All rights reserved.