Covering 2-connected 3-regular graphs with disjoint paths

摘要

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 G 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 remvoen/10. In this article, we confirm this conjecture.