English

Covering 2-connected 3-regular graphs with disjoint paths

Combinatorics 2018-06-20 v1

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)p(G) of graph GG is the cardinality of a path cover with the minimum number of paths. Reed in 1996 conjectured that a 22-connected 33-regular graph has path cover number at most n/10\lceil n/10\rceil. In this paper, we confirm this conjecture.

Keywords

Cite

@article{arxiv.1806.07014,
  title  = {Covering 2-connected 3-regular graphs with disjoint paths},
  author = {Gexin Yu},
  journal= {arXiv preprint arXiv:1806.07014},
  year   = {2018}
}
R2 v1 2026-06-23T02:34:06.196Z