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- W4307183205 abstract "Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $[n]:=left{1, ldots, nright}$ with $m=m(n)$ edges. We show that in the sparse regime, when $m/nleq 1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values. In contrast, this is not true anymore in the dense regime, when $m/n>1$, where the maximum degree of $P(n,m)$ is not concentrated on any subset of $[n]$ with bounded size." @default.
- W4307183205 created "2022-10-29" @default.
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- W4307183205 date "2021-04-30" @default.
- W4307183205 modified "2023-09-25" @default.
- W4307183205 title "Concentration of maximum degree in random planar graphs" @default.
- W4307183205 doi "https://doi.org/10.48550/arxiv.2104.14790" @default.
- W4307183205 hasPublicationYear "2021" @default.
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