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File:Prism-vf-color.svg

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English: Simultaneously coloring the vertices and faces of a 1-planar graph may require at most six colors — for instance, in this triangular prism, no two of the 11 adjacent features of the same type (5 faces and 6 vertices) may take the same colors along an edge (shown here using an black color not counted), and no two of the 18 connection pairs of vertices and faces may take the same colors. Ringel conjectured in 1965 that six colors always suffice; this was proven in 1984 by Borodin. This coloring problem formed the inspiration for 1-planar graphs.
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Author David Eppstein
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  • Apparently similar, but represents a planar graph differentiating only the visible faces (discs or polygons with eroded corners).
    Apparently similar, but represents a planar graph differentiating only the visible faces (discs or polygons with eroded corners).

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current06:42, 21 January 2013Thumbnail for version as of 06:42, 21 January 2013270 × 198 (2 KB)David Eppstein (talk | contribs)User created page with UploadWizard

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