An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E ∪F so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3): [21][22][23][24][25][26][27][28][29][30][31][32][33] 1994] proved that every plane graph of max
Maximum Face-Constrained Coloring of Plane Graphs
✍ Scribed by Radhika Ramamurthi; Douglas B. West
- Book ID
- 108497961
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 398 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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Borodin, O.V., Cyclic coloring of plane graphs, Discrete Mathematics 100 (1992) 281-289. Let G be a plane graph, and let x,(G) be the minimum number of colors to color the vertices of G so that every two of them which lie in the boundary of the same face of the size at most k, receive different colo
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It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with A ~< 3 can be colored by six colors.