Short proofs of classical theorems

We give proofs of Ore's theorem on Hamilton circuits, Brooks' theorem on vertex coloring, and Vizing's theorem on edge coloring, as well as the Chvátal-Lovász theorem on semi-kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orientations of graphs. These proofs, while not radically different from existing ones, are perhaps simpler and more natural. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 159–165, 2003