We consider a simple graph G =(V; E). The well known Path Cover problem (https://en.wikipedia.org/wiki/Path_cover) is NP-complete on all graph classes on which the Hamiltonian path problem is NP-complete, including planar graphs, bipartite graphs and chordal graphs. Many polynomial algorithms have been proposed in the literature for special graph classes on which this problem is polynomial, but I did not find any exact methods to find the minimum vertex-disjoint path cover for bipartite graphs (or even for planar graphs and chordal graphs), especially Branch and Bound Algorithms.
Do you know any exact methods, in particular Branch and Bound algorithms, for the path cover problem on graph classes on which this problem is NP-hard (bipartite graphs, planar graphs and chordal graphs)?
Thank you in advance.
