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 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}
}