Partitioning regular graphs into equicardinal linear forests (Q1174174)

\textit{J. Akiyama, G. Exoo} and \textit{F. Harary} [Math. Slovaca 30, 405--417 (1980; Zbl 0458.05050)] showed that every 3-regular graph has a partition of the edge set into two linear forests. They [Networks 11, 69--72 (1981; Zbl 0479.05027)] also showed that the edge set of a 4-regular graph can be partitioned into three linear forests. The authors show that these results hold even when the forests all are required to have the same edge cardinality (assuming the original edge cardinality satisfies an obvious necessary congruence). The conjecture by the first author, \textit{C. Colbourn} and \textit{D. Holton} [Problem 13, Ars Comb. 23A, 332--334 (1987)] that the edge set of a 3-regular graph with an even number of edges can be partitioned into two isomorphic linear forests remains open.