Steinberg's conjecture on 3-coloring planar graphs without 4- or 5-cycles
A planar graph is a graph that can be embedded in the plane. Steinberg's conjecture. Every planar graph with no cycles of length four or five is -colorable. Steinberg's conjecture was recently disproved by Cohen-Addad, Hebdige, Kráľ, Li, and Salgado; related results establish -colorability under the stronger condition excluding cycles of lengths four through seven.
References
Primary source
Luke Postle and Robin Thomas, “Hyperbolic families and coloring graphs on surfaces”, arXiv:1609.06749 (2018).
Additional references
6 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:1409.4054, arXiv:1407.5138, arXiv:1208.3395, arXiv:1004.0582.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.