Doing some random readings, also trying to revive the blog :(

**Conjecture**[Thomas]**.**For any t, any sufficiently large t-connected graph with no -minor can be made planar by removing exactly t-5 vertices.

The case when t=6 has been proven. [Kawarabayashi-Norine-Thomas-Wollan ’12]- In a subgraph-closed graph family, having polynomial expansion is equivalent to having sublinear separator. [Dvořák-Norine ’15]
**Richter-Thomassen Conjecture**, now**Pach-Rubin-Tardos Theorem**, states that the total number of intersections between n pairwise intersecting Jordan curves in the plane, no three pass through the same point, is at least .

**Main Theorem**[Pach-Rubin-Tardos ’15]**.**Consider the above set of Jordan curves. Then the number of crossing points is times the number of touching points, those that are the only intersection between two Jordan curves.- Further results on arc and bar k-visibility graphs by Sawhney and Weed, 2016.
- Minimum cut of directed planar graphs in O(n log log n) time by Mozes, Nikolaev, Nussbaum, and Weimann, 2015.
- The weakly simple polygon result has been extended to geometric intersection numbers. [Despré-Lazarus ’15]

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