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

Johannes H. Hattingh (), Osama A. Saleh, Lucas C. Merwe and Terry J. Walters
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Johannes H. Hattingh: East Carolina University
Osama A. Saleh: University of Tennessee at Chattanooga
Lucas C. Merwe: University of Tennessee at Chattanooga
Terry J. Walters: University of Tennessee at Chattanooga

Journal of Combinatorial Optimization, 2012, vol. 24, issue 3, No 12, 329-338

Abstract: 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 .

Keywords: Nordhaus-Gaddum; Induced path number (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9388-0

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