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Projective‐planar graphs with even duals
Author(s) -
Negami Seiya
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160402
Subject(s) - mathematics , bipartite graph , combinatorics , projective plane , planar graph , dual polyhedron , projective test , embedding , planar , planar straight line graph , real projective plane , pencil (optics) , discrete mathematics , collineation , graph , projective space , 1 planar graph , pure mathematics , line graph , geometry , computer science , physics , artificial intelligence , optics , computer graphics (images) , correlation
Let G be a connected graph which is projective‐planar but is not planar. It will be shown that G can be embedded in the projective plane so that it has only even faces if and only if either G is bipartite or its canonical bipartite covering is planar and that such an embedding is unique if G is 3‐connected.