AbstractWe show an O(1.344n)=O(20.427n) algorithm for edge-coloring an n-vertex graph using three colors. Our algorithm uses polynomial space. This improves over the previous O(2n/2) algorithm of Beigel and Eppstein [R. Beigel, D. Eppstein, 3-coloring in time O(1.3289n), J. Algorithms 54 (2) (2005) 168–204.]. We apply a very natural approach of generating inclusion–maximal matchings of the graph. The time complexity of our algorithm is estimated using the “measure and conquer” technique.