Minimally k-connected graphs of low order and maximal size |
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Authors: | Cai Mao-cheng |
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Institution: | Institute of Mathematics, Academia Sinica, Peking, The People''s Republic of China |
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Abstract: | Let G be a minimally k-connected graph of order n and size e(G).Mader 4] proved that (i) ; (ii) e(G)?k(n?k) if n?3k?2, and the complete bipartite graph Kk,n?k is the only minimally k-connected graph of order; n and size k(n?k) when k?2 and n?3k?1.The purpose of the present paper is to determine all minimally k-connected graphs of low order and maximal size. For each n such that k+1?n?3k?2 we prove and characterize all minimally k-connected graphs of order n and size . |
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