On the Maximum Degree of a Random Planar Graph
2008 ◽
Vol 17
(4)
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pp. 591-601
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Let the random graphRnbe drawn uniformly at random from the set of all simple planar graphs onnlabelled vertices. We see that with high probability the maximum degree ofRnis Θ(lnn). We consider also the maximum size of a face and the maximum increase in the number of components on deleting a vertex. These results extend to graphs embeddable on any fixed surface.
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2014 ◽
Vol 23
(4)
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pp. 551-570
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2018 ◽
Vol 10
(04)
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pp. 1850044
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