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My Favorite Domination Conjectures in Graph Theory Are Bounded

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Graph Theory

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Abstract

For a graph G of order n and a parameter ϑ(G), if ϑ(G) ≤ \(\frac{a} {b}\) n for some rational number \(\frac{a} {b}\), where 0 < \(\frac{a} {b}\) < 1, then we refer to this upper bound on ϑ(G) as an \(\frac{a} {b}\)-bound on ϑ(G). In this chapter, we present over twenty \(\frac{a} {b}\)-bound conjectures on domination type parameters.

Research supported in part by the South African National Research Foundation and the University of Johannesburg

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park, Johannesburg, 2006, South Africa

    Michael A. Henning

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  1. Michael A. Henning
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Correspondence to Michael A. Henning .

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Editors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, California, USA

    Ralucca Gera

  2. School of Computing, Clemson University, Clemson, South Carolina, USA

    Stephen Hedetniemi

  3. Department of Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA

    Craig Larson

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Henning, M.A. (2016). My Favorite Domination Conjectures in Graph Theory Are Bounded. In: Gera, R., Hedetniemi, S., Larson, C. (eds) Graph Theory. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-31940-7_15

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