# Vertex partitions of ($C 3 , C 4 , C 6$) -free planar graphs

2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A graph is (k 1 , k 2)-colorable if its vertex set can be partitioned into a graph with maximum degree at most k 1 and and a graph with maximum degree at most k 2. We show that every (C 3 , C 4 , C 6)-free planar graph is (0, 6)-colorable. We also show that deciding whether a (C 3 , C 4 , C 6)-free planar graph is (0, 3)-colorable is NP-complete.
Document type :
Journal articles

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### Citation

François Dross, Pascal Ochem. Vertex partitions of ($C 3 , C 4 , C 6$) -free planar graphs. Discrete Mathematics, Elsevier, 2019, 342 (11), pp.3229-3236. ⟨10.1016/j.disc.2019.07.002⟩. ⟨hal-02990467⟩

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