Liu, Yan; Ma, Yinghong Maximal non-ID-factor-critical graphs. (English) Zbl 1045.05072 J. Math. Study 36, No. 4, 374-378 (2003). Summary: We say that a simple graph \(G\) is independent-set-deletable factor-critical, shortly ID-factor-critical, if for every independent set \(I\) of \(G\) whose size has the same parity with \(| V(G)|\), \(G-I\) has a perfect matching. A simple graph \(G\) is maximal non-ID-factor-critical if \(G\) is not ID-factor-critical and \(G+xu\) is ID-factor-critical for every two nonadjacent vertices \(x\) and \(y\). In this paper, we characterize the maximal non-ID-factor-critical graphs. MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:independent set PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Ma}, J. Math. Study 36, No. 4, 374--378 (2003; Zbl 1045.05072)