Strong Bordeaux Conjecture on 3-coloring planar graphs
Let be a planar graph. Strong Bordeaux Conjecture. If no pair of cycles of length three in shares an edge and has no cycle of length five, then is 3-colorable. This conjecture is explicitly stated to be disproved by the same counterexample that disproves Steinberg's conjecture.
References
Primary source
Vincent Cohen-Addad, Michael Hebdige, Daniel Kral, Zhentao Li and Esteban Salgado, “Steinberg's Conjecture is false”, arXiv:1604.05108 (2016).
Additional references
3 papers in this index state this conjecture (2010–2016). The statement above is taken from the most recent of them; the others are arXiv:1508.07890, arXiv:1004.0582.
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