Covering 2‐connected 3‐regular graphs with disjoint paths
Gexin Yu · Journal of Graph Theory · 2017
Abstract A path cover of a graph is a set of disjoint paths so that every vertex in the graph is contained in one of the paths. The path cover number of graphGis the cardinality of a path cover with the minimum number of paths. Reed in 1996 conjectured that a 2‐connected 3‐regular graph has path cover number at most . In this article, we confirm this conjecture.