1. A relaxation of the Bordeaux Conjecture.
- Author
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Liu, Runrun, Li, Xiangwen, and Yu, Gexin
- Subjects
- *
RELAXATION methods (Mathematics) , *LOGICAL prediction , *GRAPH theory , *GRAPH coloring , *MATHEMATICAL mappings , *MATHEMATICAL proofs - Abstract
A ( c 1 , c 2 , … , c k ) -coloring of a graph G is a mapping φ : V ( G ) ↦ { 1 , 2 , … , k } such that for every i , 1 ≤ i ≤ k , G [ V i ] has maximum degree at most c i , where G [ V i ] denotes the subgraph induced by the vertices colored i . Borodin and Raspaud conjecture that every planar graph with neither 5 -cycles nor intersecting triangles is 3 -colorable. We prove in this paper that every planar graph with neither 5 -cycles nor intersecting triangles is (2, 0, 0)-colorable. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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