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JOURNALS // Diskretnyi Analiz i Issledovanie Operatsii // Archive

Diskretn. Anal. Issled. Oper., 2023 Volume 30, Issue 4, Pages 91–109 (Mi da1335)

A complete complexity dichotomy of the edge-coloring problem for all sets of 8-edge forbidden subgraphs

D. S. Malyshevab, O. I. Duginovc

a National Research University “Higher School of Economics”, 25/12 Bolshaya Pechyorskaya Street, 603155 Nizhny Novgorod, Russia
b Lobachevsky Nizhny Novgorod State University, 23 Gagarin Avenue, 603950 Nizhny Novgorod, Russia
c Belarusian State University, 4 Nezavisimost Avenue, 220030 Minsk, Belarus

Abstract: For a given graph, the edge-coloring problem is to minimize the number of colors sufficient to color all the graph edges so that any adjacent edges receive different colors. For all classes defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is known. In this paper, we obtain a similar result for all sets of 8-edge prohibitions. Illustr. 2, bibliogr. 38.

Keywords: edge-coloring problem, computational complexity, monotone class.

UDC: 519.17

Received: 24.11.2022
Revised: 10.06.2023
Accepted: 22.06.2023

DOI: 10.33048/daio.2023.30.758


 English version:
Journal of Applied and Industrial Mathematics, 2023, 17:4, 791–801


© Steklov Math. Inst. of RAS, 2024