Geodesic
Some cases of polynomial solvability for~the~edge~colorability problem generated by~forbidden $8$-edge subcubic forests
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 2, pp. 38-61

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The edge-coloring problem, is to minimize the number of colors sufficient to color all the edges of a given graph so that any adjacent edges receive distinct colors. For all the classes defined by sets of forbidden subgraphs with 7 edges each, the complexity status of this problem is known. In this paper, we consider the case of prohibitions with 8 edges. It is not hard to see that the edge-coloring problem is NP-complete for such a class if there are no subcubic forests among its 8-edge prohibitions. We prove that forbidding any subcubic 8-edge forest generates a class with polynomial-time solvability of the edge-coloring problem, except for the cases formed by the disjunctive sum of one of 4 forests and an empty graph. For all the remaining four cases, we prove a similar result for the intersection with the set of graphs of maximum degree at least four. Illustr. 2, bibliogr. 14.
Mots-clés : monotone class
Keywords: edge-coloring problem, computational complexity. 
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     author = {D. S. Malyshev and O. I. Duginov},
     title = {Some cases of polynomial solvability for~the~edge~colorability problem generated by~forbidden $8$-edge subcubic forests},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {38--61},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2022_29_2_a2/}
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D. S. Malyshev; O. I. Duginov. Some cases of polynomial solvability for~the~edge~colorability problem generated by~forbidden $8$-edge subcubic forests. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 2, pp. 38-61. http://geodesic.mathdoc.fr/item/DA_2022_29_2_a2/