Some cases of polynomial solvability for the edge colorability problem generated by forbidden $8$-edge subcubic forests

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.