**Balanced circle packings for planar graphs**.

M. J. Alam, D. Eppstein, M. T. Goodrich, S. Kobourov, and S. Pupyrev.

arXiv:1408.4902.

*22nd Int. Symp. Graph Drawing*, Würzburg, Germany, 2014.

Springer,*Lecture Notes in Comp. Sci.*8871, 2014, pp. 125–136.The balanced circle packings of the title are systems of interior-disjoint circles, whose tangencies represent the given graph, and whose radii are all within a polynomial factor of each other. We show that these packings always exist for trees, cactus graphs, outerpaths, k-outerplanar graphs of bounded degree when k is at most logarithmic, and planar graphs of bounded treedepth. The treedepth result uses a new construction of inversive-distance circle packings.

**Contact graphs of circular arcs**.

M. J. Alam, D. Eppstein, M. Kaufmann, S. Kobourov, S. Pupyrev A. Schulz, and T. Ueckerdt.

arXiv:1501.00318.

14th Algorithms and Data Structures Symp. (WADS 2015), Victoria, BC.

Springer,*Lecture Notes in Comp. Sci.*9214 (2015), pp. 1–13.We study the graphs formed by non-crossing circular arcs in the plane, having a vertex for each arc and an edge for each point where an arc endpoint touches the interior of another arc.

(Slides)

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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