Crossref Citations
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Sedláček, J.
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Published online by Cambridge University Press: 17 April 2009
The local connectivity, νk(G), of a graph G is the minimum of the connectivities of neighbourhoods of the vertices of G. G is minimally locally n-connected if νk(G) = n and for every edge x of G, νk(G−x) = n − 1. A necessary and sufficient condition for a locally connected graph to be minimally locally 1-connected is given, and it is shown that for n ≥ 7, is minimally locally 1-connected.