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    Article

    On k- critical 2k- connected graphs

    A graph G is called an (n,k)-graph if κ(G-S)=n-|S| for any S ⊆ V(G) with |S| ≤ k, where ?(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2?(1-factor) is the uniqu...

    Jianji Su, Xudong Yuan, Qiaofeng Zhao in Science in China Series A: Mathematics (2003)

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    Article

    (3,k)-Factor-Critical Graphs and Toughness

     A graph is (r,k)-factor-critical if the removal of any set of k vertices results in a graph with an r-factor (i.e. an r-regular spanning subgraph). Let t(G) denote the toughness of graph G. In this paper, we sho...

    Minýong Shi, Xudong Yuan, Mao-cheng Cai, Odile Favaron in Graphs and Combinatorics (1999)