Maximal Planar Subgraphs of Fixed Girth in Random Graphs

Manuel Fernández, Nicholas Sieger, Michael Tait

Abstract


In 1991, Bollobás and Frieze showed that the threshold for $G_{n,p}$ to contain a spanning maximal planar subgraph is very close to $p = n^{-1/3}$. In this paper, we compute similar threshold ranges for $G_{n,p}$ to contain a maximal bipartite planar subgraph and for $G_{n,p}$ to contain a maximal planar subgraph of fixed girth $g$.

 


Keywords


Planar subgraph; Random graph; Threshold

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