It is shown that a \(4\)-critical planar graph must contain a cycle of length \(4\) or \(5\) or a face of size \(k\), where \(6 \leq k \leq 11\).
Citation
HL. Abbott, B. Zhou. On Small Faces in 4-critical Planar Graphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 032. 203-207. DOI: .