(1) A heuristic algorithm to find a near-optimal solution to the traveling salesman problem. Step 1: find a minimum spanning tree T. Step 2: find a perfect matching M among vertices with odd degree. Step 3: combine the edges of M and T to make a multigraph G. Step 4: find an Euler cycle in G by skipping vertices already seen. (2) An algorithm to find the chromatic number of a graph.