ON MAX CUT IN CUBIC GRAPHS

Abstract This paper is concerned with the maximum cut problem in parallel on cubic graphs. New theoretical results characterizing the cardinality of the cut are presented. These results make it possible to design a simple combinatorial O(log n) time parallel algorithm, running on a CRCW P-RAM with O(n) processors. The approximation ratio achieved by the algorithm is 1·3 and improves the best known parallel approximation ratio, i.e. 2, in the special class of cubic graphs. The algorithm also guarantees that the size of the returned cut is at least ((9g −3)/8 g)n, where g is the odd girth of the input graph. Experimental results round off the paper, showing that the solutions obtained in practice are likely to be much better than the theoretical lower bound.