Conic reduction of graphs for the stable set problem Original Research Article

We introduce a new kind of graph transformations reducing the graph stability number by one. The area of applicability for these transformations is characterized by two forbidden-induced subgraphs. Based on the proposed transformations, we derive a new polynomially solvable case for the maximum stable set problem in a particular subclass of chair-free graphs, where a chair is the graph with vertices 1,2,3,4,5 and edges (1,2),(1,3),(1,4),(4,5).