EveryK1,7andK1,3-free, 3-vertex critical graph of even order has a perfect matching
Adel P. Kazemi · Journal of Discrete Mathematical Sciences and Cryptography · 2010
Ananchuen and Plummer in [Matchings in 3-vertex-critical graphs: the even case, Networks, Vol. 45 (4) (2005), pp. 210–213] began the study of matchings in 3-vertex-critical graphs. They showed that any 3-vertex-critical graph on an even number of vertices which is K 1,5-free must have a perfect matching. Also they conjectured that this is also true when G is K 1,7-free. In the present paper we prove this conjecture when G is triangle-free.