Partitions of digraphs into paths or circuits
The paper considers the problem of partitioning the arcs of a digraph into elementary paths or circuits. It is conjectured that the arcs of a digraph can be partitioned into \(\alpha\) or fewer elementary paths or circuits where \(\alpha\) is the minimum number of a demi-cocycle. It is shown that the arcs of a pseudo-symmetric digraph or an acircuitous digraph can be partitioned into \(\alpha\) or fewer circuits. Furthermore, the arcs of a bipartite digraph can be partitioned into \(\alpha\) paths or circuits of length at most two and this bound is the best possible.
scientific article; zbMATH DE number 3977028
scientific article