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

Doost Ali Mojdeh () and Babak Samadi ()
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Doost Ali Mojdeh: University of Mazandaran
Babak Samadi: University of Mazandaran

Journal of Combinatorial Optimization, 2019, vol. 38, issue 3, No 7, 739-747

Abstract: 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 $$\rho _{o}(G)=n-\omega (G)$$ ρ o ( G ) = n - ω ( G ) posed in Hamid and Saravanakumar (Discuss Math Graph Theory 35:5–16, 2015).

Keywords: Packing number; Open packing number; Nordhaus–Gaddum inequality; Open problem; Triangle-free graph; 05C69 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-019-00410-4

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