Mader’s Conjecture On Extremely Critical Graphs

A non-complete graph G is called an (n,k)-graph if it is n-connected but GX is not (n−|X|+1)-connected for any X V (G) with |X|≤k. Mader conjectured that for k≥3 the graph K2k+2−(1−factor) is the unique (2k,k)-graph(up to isomorphism).

Here we prove this conjecture.

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Correspondence to Dr. Matthias Kriesell.

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Kriesell, M. Mader’s Conjecture On Extremely Critical Graphs. Combinatorica 26, 277–314 (2006). https://doi.org/10.1007/s00493-006-0017-y

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Mathematics Subject Classification (2000):

  • 05C40
  • 05C35
  • 05C75