Corrigendum to Proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs: [J. Combin. Theory Ser. B 91 (2004) 301-325]

We correct an error in the proof of the main theorem. At the beginning of the proof of Lemma 8, the sentence reads “Let be the fifth vertex of anA that containsv5v4v2v11. Clearly is outside ′ ∪ { , }.’’As pointed out by an anonymous referee, this statement is not true because every vertex in S4 can serve as . Observe that in Lemma 8, the adjacency properties (i) and (iii) satisfied by are also enjoyed by any vertex inS4. What we are about to do in this corrected version is to simply delete Lemma 8 and replace with a vertex inS4. To be specific, the error can be fixed by making the following changes: 1. Delete the original Lemma 8 and its proof; now the original Lemma 9 becomes Lemma 8 (delete in the third line of its proof). 2. Replace the first paragraph of Section 4 “Proof of the Theorem’’ with the following: “Let s4 be a vertex inS4. From Lemmas 7 and 8 we deduce that v2s4 v7 is aP4, so by hypothesis it is contained in an A; let be the fifth vertex of thisA. It is easy to see that ∈ ′ ∪ S ∪ { , }. Since{s4v8v10; , s3, s2} = F for anys2 ∈ S2 ands3 ∈ S3, one of the following four cases must occur:’’ 3. Replace contained in line 5 (p. 323) with s4.