An algorithm for the decomposition of graphs into cliques

Abstract

AbstractChung (F. R. K. Chung, On the decomposition of graphs, SIAM J. Algebraic Discrete Methods 23 (1981), 1–12.) and independently Györi and Kostochka (E. Györi and A. V. Kostochka, On a problem of G. O. H. Katona and T. Tarján, Acta Math. Acad. Sci. Hung. 34 (1979), 321–327.) proved the following theorem: For any graph G with n vertices, the edge set E(G) can be decomposed into cliques such that the sum of the orders of the cliques is at most ⌊n2/2⌋. In this paper, we give a polynomial algorithm for the decomposition of E(G) into cliques which satisfies the condition of the theorem. The time required for this algorithm is at most O(n3). The algorithm may be regarded as a support for Winkler's conjecture posed in P. Winkler (Problem 27, Discrete Math. 101 (1992), 359–360). © 1995, John Wiley & Sons, Inc.