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A Nordhaus-Gaddum-type result for the induced path number

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Abstract

The induced path number ρ(G) of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a graph. A Nordhaus-Gaddum-type result is a (tight) lower or upper bound on the sum (or product) of a parameter of a graph and its complement. If G is a subgraph of H, then the graph H−E(G) is the complement of G relative to H. In this paper, we consider Nordhaus-Gaddum-type results for the parameter ρ when the relative complement is taken with respect to the complete bipartite graph K n,n .

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Authors and Affiliations

  1. Department of Mathematics, East Carolina University, Greenville, NC, 27858, USA

    Johannes H. Hattingh

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    Osama A. Saleh, Lucas C. van der Merwe & Terry J. Walters

Authors
  1. Johannes H. Hattingh
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  2. Osama A. Saleh
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  3. Lucas C. van der Merwe
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  4. Terry J. Walters
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Correspondence to Johannes H. Hattingh.

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Hattingh, J.H., Saleh, O.A., van der Merwe, L.C. et al. A Nordhaus-Gaddum-type result for the induced path number. J Comb Optim 24, 329–338 (2012). https://doi.org/10.1007/s10878-011-9388-0

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  • DOI: https://doi.org/10.1007/s10878-011-9388-0

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