Просмотр кода страницы Locally k-connected graph

'''Locally <math>k</math>-connected graph''' --- локально <math>k</math>-связный граф. 

Let <math>M</math> and <math>H</math> be two subgraphs of <math>G</math> with <math>V(H) \cap V(M) =
\emptyset</math>. We say that <math>H</math> is '''locally <math>k</math>-connected to <math>M</math> in <math>G</math>''' if <math>G</math> contains <math>k</math> pairwise disjoint <math>(x,V(M))</math> paths for every
vertex <math>x \in H</math>. Let now <math>M</math> be a cycle in <math>G</math>, and let <math>H</math> be a
subgraph of <math>G - V(M)</math>. We say that <math>M</math> is '''locally longest with respect to <math>H</math> in <math>G</math>''' if we cannot obtain a cycle longer than <math>M</math> by
replacing a ''segment'' <math>M[u,v]</math> by a <math>(u,v)</math>-path of <math>G</math> through <math>H</math>.