## Drawing Graphs in the Plane with a Prescribed Outer Face and Polynomial Area

We study the classic graph drawing problem of drawing a planar graph using straight-line edges with a prescribed convex polygon as the outer face. Unlike previous algorithms for this problem, which may produce drawings with exponential area, our method produces drawings with polynomial area. In addition, we allow for collinear points on the boundary, provided such vertices don't create overlapping edges. Thus, we solve an open problem of Duncan et al., which, when combined with their work, implies that we can produce a planar straight-line drawing of a combinatorially-embedded genus-g graph with the graph's canonical polygonal schema drawn as a convex polygonal external face.

keywords: Computational Geometry, Graph Drawing, Graphs Theory

### Journal Article (peer-reviewed)

David Eppstein, Erin W. Chambers, Maarten Löffler, Michael T. Goodrich

Drawing Graphs in the Plane with a Prescribed Outer Face and Polynomial Area

Journal of Graph Algorithms and Applications

16, 2, 243–259, 2012

### Conference Proceedings (peer-reviewed)

David Eppstein, Erin W. Chambers, Maarten Löffler, Michael T. Goodrich

Drawing Graphs in the Plane with a Prescribed Outer Face and Polynomial Area

Proc. 18th Symposium on Graph Drawing

LNCS 6502, 129–140, 2011

### Archived Publication (not reviewed)

David Eppstein, Erin W. Chambers, Maarten Löffler, Michael T. Goodrich

Drawing Graphs in the Plane with a Prescribed Outer Face and Polynomial Area

1009.0088, 2010

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