Abstract
This paper generalizes previous works on perfectly orderable graphs by Olariu (Discrete Math. 113 (1992) 143) and by Hoàng et al. (Discrete Math. 102 (1992) 67). Chvátal defined a graph to be perfectly orderable (V. Chvátal, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, Annals of Discrete Mathematics, Vol. 21, North-Holland, Amsterdam, 1984, pp. 63–65) if there exists a linear order < on its set of vertices such that no induced path abcd with edges ab, bc, cd has both a< b and d< c. Given a graph G and a vertex v in G such that G− v is perfectly orderable, we set some conditions on v for which we deduce that G is perfectly orderable. Our method allows to construct a new class of such graphs, recognizable in polynomial time, containing quasi-brittle graphs, charming graphs and some other classes of perfectly orderable graphs.
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