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Journal Articles Ars Mathematica Contemporanea Year : 2011

Facial parity edge colouring


A facial parity edge colouring of a connected bridgeless plane graph is an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same colour, in addition, for each face α and each colour c, either no edge or an odd number of edges incident with α is coloured with c. From Vizing's theorem it follows that every 3-connected plane graph has a such colouring with at most Δ* + 1 colours, where Δ* is the size of the largest face. In this paper we prove that any connected bridgeless plane graph has a facial parity edge colouring with at most 92 colours.
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inria-00634947 , version 1 (09-11-2011)


  • HAL Id : inria-00634947 , version 1


Július Czap, Stanislav Jendrol', František Kardoš. Facial parity edge colouring. Ars Mathematica Contemporanea, 2011, 4 (2), pp.255-269. ⟨inria-00634947⟩
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