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

Author

Listed:
  • Doost Ali Mojdeh

    (University of Mazandaran)

  • Babak Samadi

    (University of Mazandaran)

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).

Suggested Citation

  • Doost Ali Mojdeh & Babak Samadi, 2019. "Packing parameters in graphs: new bounds and a solution to an open problem," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 739-747, October.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:3:d:10.1007_s10878-019-00410-4
    DOI: 10.1007/s10878-019-00410-4
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    Cited by:

    1. Xuqing Bai & Hong Chang & Xueliang Li, 2020. "More on limited packings in graphs," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 412-430, August.
    2. Xuqing Bai & Hong Chang & Xueliang Li, 0. "More on limited packings in graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.

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