Packing parameters in graphs: new bounds and a solution to an open problem, By Doost Ali Mojdeh

Research

Title	Packing parameters in graphs: new bounds and a solution to an open problem
Type	Article
Keywords	Packing number, Open packing number, Nordhaus–Gaddum inequality, Open problem, Triangle-free graph
Journal	JOURNAL OF COMBINATORIAL OPTIMIZATION
DOI	https://doi.org/10.1007/s10878-019-00410-4
Researchers	Doost Ali Mojdeh (First researcher) , Babak Samadi (Second researcher)

Abstract

In this paper,we investigate the packing parameters in graphs.By applying theMantel’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) = n − ω(G) posed in Hamid and Saravanakumar (Discuss Math Graph Theory 35:5–16, 2015).