A note on the three color problem
In 1990 Paul Erdős asked: Is there an integer \(k\geq 5\) such that if \(G\) is a planar graph without \(i\)-circuits, \(4\leq i\leq k\), then \(G\) is 3- colorable? A year later H. L. Abbott and B. Zhou answered this question affirmatively by proving the above with \(k= 11\). This note strengthens their result by showing that \(G\) is 3-colorable, if it is planar without \(i\)-circuits for \(i\) from 4 through 9.
scientific article; zbMATH DE number 754153
scientific article