The complexity of Shortest Common Supersequence for inputs with no identical consecutive letters

The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and Johnson] is NP-complete. Many variants have been studied in the literature. In this paper we settle the complexity of two such variants of SCS where inputs do not contain identical consecutive letters. We prove that those variants denoted \varphi SCS and MSCS both have a decision version which remains NP-complete when |\Sigma| is at least 3. Note that it was known for MSCS when |\Sigma| is at least 4 [Fleisher and Woeginger] and we discuss how [Darte] states a similar result for |\Sigma| at least 3.