Simultaneously Colouring the Edges and Faces of Plane Graphs

Waller, Adrian

doi:10.1006/jctb.1997.1725

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Introduction4

Application To Simultaneous Edge-face Coloring Of Plane Graphs1

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Cited by 28 publications

(12 citation statements)

References 7 publications

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“…Mel'nikov [11] conjectured that every plane graph of maximum degree has a ( +3)-edge-face coloring . This was proved by Borodin [2,4] for ≤ 3 and ≥ 8, and the general case was proved by Waller [15], and independently by Sanders and Zhao [12]. In fact, Borodin [4] proved the upper bound of +1 for plane graphs of maximum degree ≥ 10.…”

Section: Introductionmentioning

confidence: 83%

Edge-face coloring of plane graphs with maximum degree nine

Sereni

Stehlı́k

2010

J. Graph Theory

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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 maximum degree ≥ 10 can be edge-face colored with +1 colors. We extend Borodin's result to the case where = 9. ᭧

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Section: Introductionmentioning

confidence: 83%

Edge-face coloring of plane graphs with maximum degree nine

Sereni

Stehlı́k

2010

J. Graph Theory

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“…Borodin [3] (see also [6]) proved Ringel's conjecture [15] that v vf D 6. The authors [17] (see also [24]) proved Melnikov's conjecture [14] that v ef D D 3.…”

Section: Introductionmentioning

confidence: 99%