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On small faces in 4-critical planar graphs. (English) Zbl 0755.05062
Summary: 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 $$6\leq k\leq 11$$.

##### MSC:
 05C38 Paths and cycles
##### Keywords:
small faces; planar graphs; cycle