Clique Coverings of Complements of Paths and Cycles

Let cc(▪) be the minimum number of complete subgraphs necessary to cover the edges of the complement of a graph G. When G is a path or cycle of length n, exact values of cc(▪) are found for small n and bounds are determined implying that cc(▪) is of order log n. Logarithmic bounds on cc(▪) are given for the more general class of those graphs G whose n vertices each have degree 1 or 2. This continues previous work in which cc(▪) was determined for perfect matchings G.