On Plick Graphs with Coarseness Number One

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 K3,3 or K5. In this paper, we obtain a necessary and sufficient condition for plick graph Pn(G); n ≥ 1 to have coarseness number one. 
DOI: 10.1007/s11786-011-0079-0

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