Multiple vertex coverings by specified induced subgraphs

Given graphs H-1,..., H-k, let f(H-1,..., H-k) be the minimum order of a gr aph G such that for each i, the induced copies of H-i in G cover V(G). We p rove constructively that f(H-1, H-2) less than or equal to 2(n(H-1) + n(H-2 ) - 2); equality holds when H-1 =(H) over bar(2) = K-n. We prove that f(H-1 ,(K) over bar(n),)= n + 2 root delta(H-1)n + O(1) as n --> infinity. We als o determine f(K-1,K-m-1, (K) over bar(n)) exactly. (C) 2000 John Wiley & So ns, Inc.