Covering 2‐connected 3‐regular graphs with disjoint paths.

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 p ( G ) of graph <italic>G</italic> is 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 ⌈ n / 10 ⌉. In this article, we confirm this conjecture. [ABSTRACT FROM AUTHOR]