Efficiently list‐edge coloring multigraphs asymptotically optimally

We give polynomial time algorithms for the seminal results of Kahn, who showed that the Goldberg–Seymour and list‐coloring conjectures for (list‐)edge coloring multigraphs hold asymptotically. Kahn's arguments are based on the probabilistic method and are non‐constructive. Our key insight is th...

Full description

Saved in:
Bibliographic Details
Published inRandom structures & algorithms Vol. 61; no. 4; pp. 724 - 753
Main Authors Iliopoulos, Fotis, Sinclair, Alistair
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.12.2022
Wiley Subscription Services, Inc
Subjects
Asymptotic properties
Coloring
edge coloring
Goldberg–Seymour conjecture
Graph theory
list‐edge‐coloring conjecture
multigraphs
Polynomials
Probabilistic methods
Search algorithms
Statistical analysis
Online AccessGet full text

Cover

More Information
Summary:We give polynomial time algorithms for the seminal results of Kahn, who showed that the Goldberg–Seymour and list‐coloring conjectures for (list‐)edge coloring multigraphs hold asymptotically. Kahn's arguments are based on the probabilistic method and are non‐constructive. Our key insight is that we can combine sophisticated techniques due to Achlioptas, Iliopoulos, and Kolmogorov for the analysis of local search algorithms with correlation decay properties of the probability spaces on matchings used by Kahn in order to construct efficient edge‐coloring algorithms.
Bibliography:Funding information
NSF, CCF‐1514434; CCF‐1815328; Onassis Foundation
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21074