Maximal Planar Subgraphs of Fixed Girth in Random Graphs

Manuel Fernández; Nicholas Sieger; Michael Tait

Maximal Planar Subgraphs of Fixed Girth in Random Graphs

Combinatorics 2017-06-21 v1

Authors: Manuel Fernández , Nicholas Sieger , Michael Tait

Abstract

In 1991, Bollob\'{a}s 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

random graphs graph pebbling bipartite graphs

Cite

@article{arxiv.1706.06202,
  title  = {Maximal Planar Subgraphs of Fixed Girth in Random Graphs},
  author = {Manuel Fernández and Nicholas Sieger and Michael Tait},
  journal= {arXiv preprint arXiv:1706.06202},
  year   = {2017}
}

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