Wrapper for Boyer’s (C) planarity algorithm¶
- sage.graphs.planarity.is_planar(g, kuratowski=False, set_pos=False, set_embedding=False)[source]¶
Check whether
gis planar using Boyer’s planarity algorithm.If
kuratowskiisFalse, returnsTrueifgis planar,Falseotherwise. IfkuratowskiisTrue, returns a tuple, first entry is a boolean (whether or not the graph is planar) and second entry is a Kuratowski subgraph, i.e. an edge subdivision of \(K_5\) or \(K_{3,3}\) (if not planar) orNone(if planar). Also, will set an_embeddingattribute for the graphgifset_embeddingis set toTrue.INPUT:
kuratowski– boolean (default:False); when set toTrue, return a tuple of a boolean and eitherNoneor a Kuratowski subgraph (i.e. an edge subdivision of \(K_5\) or \(K_{3,3}\)). When set toFalse, returnsTrueifgis planar,Falseotherwise.set_pos– boolean (default:False); whether to use Schnyder’s algorithm to determine and set positionsset_embedding– boolean (default:False); whether to record the combinatorial embedding returned (seeget_embedding())
EXAMPLES:
sage: G = graphs.DodecahedralGraph() sage: from sage.graphs.planarity import is_planar sage: is_planar(G) True sage: Graph('@').is_planar() True
>>> from sage.all import * >>> G = graphs.DodecahedralGraph() >>> from sage.graphs.planarity import is_planar >>> is_planar(G) True >>> Graph('@').is_planar() True