Portal de Periódicos da CAPES

On simultaneous planar graph embeddings

2006; Elsevier BV; Volume: 36; Issue: 2 Linguagem: Inglês

10.1016/j.comgeo.2006.05.006

1879-081X

Peter Braß, Eowyn Čenek, Cristian A. Duncan, Alon Efrat, Cesim Erten, Dan Ismailescu, Stephen Kobourov, Anna Lubiw, Joseph S. B. Mitchell,

Structural Analysis and Optimization

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. We present positive and negative results for the two versions of the problem. Among the positive results with given mapping, we show that we can embed two paths on an n×n grid, and two caterpillar graphs on a 3n×3n grid. Among the negative results with given mapping, we show that it is not always possible to simultaneously embed three paths or two general planar graphs. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n2)×O(n2) grid.