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

A hypergraph H on n vertices and m edges is said to be nearly-intersecting if every edge of H intersects all but at most polylogarthmically many (in m and n) other edges. Given lists of colors L(v), for each vertex v∈V, H is said to be L-(list) colorable, if each vertex can be assigned a color from...

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Bibliographic Details
Published in:Theoretical computer science Vol. 902; pp. 64 - 75
Main Author: Elbassioni, Khaled
Format: Journal Article
Language:English
Published: Elsevier B.V 18.01.2022
Subjects:
Exact algorithms
Hypergraph coloring
Hypergraph dualization
List coloring
Quasi-polynomial algorithm
List coloring
Hypergraph dualization
Quasi-polynomial algorithm
Hypergraph coloring
Exact algorithms
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:A hypergraph H on n vertices and m edges is said to be nearly-intersecting if every edge of H intersects all but at most polylogarthmically many (in m and n) other edges. Given lists of colors L(v), for each vertex v∈V, H is said to be L-(list) colorable, if each vertex can be assigned a color from its list such that no edge in 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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2021.12.009