Efficiently list-edge coloring multigraphs asymptotically optimally

Fotis Iliopoulos, Alistair Sinclair

Abstract: We give polynomial time algorithms for the seminal results of Kahn [19, 20], 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 nonconstructive. Our key insight is that we can combine sophisticated techniques due to Achlioptas, Iliopoulos and Kolmogorov [2] 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.