Erratum to "An approximation algorithm for maximum triangle packing": [Discrete Applied Mathematics 154 (2006) 971-979]

We thank Zhi-Zhong Chen (Tokyo Denki University) for drawing our attention to the following typos in our paper. Lemma 2. (i) In the definition of E ,x the term u ∈ S should be deleted. This term should be added instead to the definitions of EC and ED . (ii) The numbers attached to the upper vertices of the first graph in the second row of Fig. 7 should be (0, 1 2 ) (instead of ( 1 2 , 0)). To facilitate understanding of the proof of Lemma 2 we would like to add the following clarifications: (i) in the stated upper bound on ̂, the conditional probabilities are over all possible mappings of the deletion pattern to the cycle with the specified and x. (ii) EC and ED are the events that u and v are ends of, respectively, a common or a different path in P. Since it is possible that u / ∈ S, the sum of probabilities of these events may be less than 1. (iii) The values attached to vertices in Fig. 7 are the values of PC and PD given that the specified vertex is mapped to v . These values are taken over the (generally) two possible cases for the location of u on the cycle, given that it is at distance from v . Theorem 1. The correct bound is 43/83. (Note that the bound for the 2-edge path packing does not change.) Some numbers appearing in the proof of Theorem 1 should be changed as follows: Originally w(M ′) (1 − )/3opt. Hence 1 4w(M ′) ≥ (1 − )/12opt. Hence the added weight is at least 1 16 (1 − ); Altogether, w(T ) ≥ [ 3 + 3 4 (1 − ) ] (1 − )opt + 1 16 (1 − )opt.