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Results tagged with random-graphs
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user 24076
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
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Accepted
Do there exist sparse graphs with large crossing number?
Take the following graph: start with the complete graph $K_5$, and replace every edge by $n/10$ paths of length $2$. The resulting graph has $n+5$ vertices, $2n$ edges, and crossing number $n^2/100$.
…
- 6,101
45
votes
Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on ap...
Assuming an unpublished Ramsey-type result by Robertson and Seymour about Kuratowski minors [FK18, Claim 5], which is now "folklore" in the graph-minor community,
an asymptotic variant of the crossing …
- 6,101