On a property of minimal triangulations

This completes the results of Parra and Scheffler, who have shown that MT holds for H=Pk, the path on k vertices, if and only if k⩽5 [A. Parra, P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics 79 (1997) 171-188], and of Meister, who proved that MT holds for ℓP2, ℓ copies of a P2, if and only if ℓ⩽2 [D. Meister, A complete characterisation of minimal triangulations of 2K2-free graphs, Discrete Mathematics 306 (2006) 3327-3333].