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