| On k-critical 2k-connected graphs |
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| 作者姓名： | 苏健基 袁旭东 赵巧凤 |
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| 作者单位： | Department of Mathematics，Guangxi Normal University，Department of Mathematics，Guangxi Normal University，Department of Mathematics，Guangxi Normal University Guilin 541004，China Correspondence should be addressed to Su Jianji，Guilin 541004，China Correspondence should be addressed to Su Jianji，Guilin 541004，China Correspondence should be addressed to Su Jianji |
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| 基金项目： | This work was supported by the National Natural Science Foundation of China
(Grant No.10171022). |
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| 摘 要： | A graph G is called an (n, k)-graph if k(G - S) = n - |S| for any S V(G) with |S| ≤ k, where k.(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.
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On k-critical 2k-connected graphs |
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| SU Jianji YUAN Xudong & ZHAO Qiaofeng.On k-critical 2k-connected graphs[J].Science in China(Mathematics),2003,46(3). |
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| Authors: | SU Jianji YUAN Xudong & ZHAO Qiaofeng |
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| Institution: | Department of Mathematics, Guangxi Normal University, Guilin 541004, China |
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| Abstract: | A graph G is called an (n,k)-graph if k(G- S) = n - |S| for any S C V(G) with |S| ≤ k,where k(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2-(1-factor) isthe unique (2k, k)-graph. Kriesell has settled two special cases for k = 3, 4. We prove the conjecture for thegeneral case k ≥ 5. |
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| Keywords: | k-critical n-connected fragment second-end |
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