3‐Coloring graphs embedded in surfaces

In this article, we show that there exists an integer k(Σ) ≥ 5 such that, if G is a graph embedded in a surface Σ without i‐circuits, 4 ≤ i ≤ k(Σ), then G is 3‐colorable. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 140–143, 2000