Admissible sequence: различия между версиями

'''Admissible sequence''' --- допустимая последовательность,

Let <math>G = (V,E)</math> be a simple undirected graph of order <math>n</math>.

that <math>n_{1} + \ldots + n_{k} = n</math>. Such a sequence will be called '''admissible''' for <math>G</math>. If <math>\tau = (n_{1}, \ldots, n_{K})</math> is an

admissible sequence for <math>G</math> and there exists a partition <math>(V_{1},

\ldots, V_{k})</math> of the vertex set <math>V</math> such that for each

<math>i \in \{1, \ldots, k\}</math>, <math>|V_{i}| = n_{i}</math> and the subgraph induced by <math>V_{i}</math> is

connected, then <math>\tau</math> is called '''realizable''' in <math>G</math> and the

sequence <math>(V_{1}, \ldots, V_{k})</math> is said to be <math>G</math>-realization of

<math>\tau</math> or a realization of <math>\tau</math> in <math>G</math>. A graph <math>G</math> is '''arbitrarily vertex decomposable''' if for each admissible sequence

<math>\tau</math> for <math>G</math> there exists a <math>G</math>-realization of <math>\tau</math>.