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On <Emphasis Type="Italic">k</Emphasis>- critical 2<Emphasis Type="Italic">k</Emphasis>- connected graphs |
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| Authors: | |
| Institution: | (1) Department of Mathematics, Guangxi Normal University, 541004 Guilin, China |
| Abstract: | 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 unique (2k, k)-graph. Kriesell has settled two special cases for k = 3,4. We prove the conjecture for the general case k ≥ 5. |
| Keywords: | k- critical n- connected fragment second-end |
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