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On Plick Graphs with Coarseness Number One

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Abstract

The coarseness ξ(G) of a graph G is the maximum number of mutually line-disjoint nonplanar subgraphs of G. Clearly, ξ(G) = 1 if and only if G is nonplanar and G has no two line-disjoint subgraphs homeomorphic to K 3,3 or K 5. In this paper, we obtain a necessary and sufficient condition for plick graph P n(G); n ≥ 1 to have coarseness number one.

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Authors and Affiliations

  1. Department of Mathematics, Karnatak University, Dharwad, 580 003, India

    Basavanagoud Bommanahal

  2. Department of Mathematics, Karnatak Arts College, Dharwad, 580 001, India

    Keerthi G. Mirajkar

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  1. Basavanagoud Bommanahal
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  2. Keerthi G. Mirajkar
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Correspondence to Keerthi G. Mirajkar.

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Bommanahal, B., Mirajkar, K.G. On Plick Graphs with Coarseness Number One. Math.Comput.Sci. 5, 7–10 (2011). https://doi.org/10.1007/s11786-011-0079-0

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  • DOI: https://doi.org/10.1007/s11786-011-0079-0

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