Steinberg's Conjecture is false
Vincent Cohen-Addad, Michael Hebdige, Daniel Kral, Zhentao Li, Esteban, Salgado
TL;DR
This paper disproves Steinberg's conjecture by providing a counterexample, showing that not all planar graphs without 4- or 5-cycles are 3-colorable.
Contribution
The paper presents the first known counterexample to Steinberg's conjecture, refuting a long-standing belief in graph theory.
Findings
Counterexample to Steinberg's conjecture provided
Planar graphs without 4- or 5-cycles are not necessarily 3-colorable
Disproves a 47-year-old conjecture
Abstract
Steinberg conjectured in 1976 that every planar graph with no cycles of length four or five is 3-colorable. We disprove this conjecture.
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