Maximal Planar Subgraphs of Fixed Girth in Random Graphs
Abstract
In 1991, Bollob\'as and Frieze showed that the threshold for Gn,p to contain a spanning maximal planar subgraph is very close to p = n-1/3. In this paper, we compute similar threshold ranges for Gn,p to contain a maximal bipartite planar subgraph and for Gn,p to contain a maximal planar subgraph of fixed girth g.
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