English

Packing parameters in graphs: New bounds and a solution to an open problem

Combinatorics 2019-08-27 v3

Abstract

In this paper, we investigate the packing parameters in graphs. By applying the Mantel's theorem, We give upper bounds on packing and open packing numbers of triangle-free graphs along with characterizing the graphs for which the equalities hold and exhibit sharp Nordhaus-Gaddum type inequalities for packing numbers. We also solve the open problem of characterizing all connected graphs with ρo(G)=nω(G)\rho_{o}(G)=n-\omega(G) posed in [S. Hamid and S. Saravanakumar, {\em Packing parameters in graphs}, Discuss Math. Graph Theory, 35 (2015), 5--16].

Keywords

Cite

@article{arxiv.1705.08667,
  title  = {Packing parameters in graphs: New bounds and a solution to an open problem},
  author = {D. A. Mojdeh and Babak Samadi},
  journal= {arXiv preprint arXiv:1705.08667},
  year   = {2019}
}
R2 v1 2026-06-22T19:57:29.407Z