Antoni Marczyk A NOTE ON ARBITRARILY VERTEX DECOMPOSABLE GRAPHS

  • Opuscula Mathematica
  • Published 2006

Abstract

A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n1, . . . , nk) of positive integers such that n1 + . . . + nk = n there exists a partition (V1, . . . , Vk) of the vertex set of G such that for each i ∈ {1, . . . , k}, Vi induces a connected subgraph of G on ni vertices. In this paper we show that if G is a two-connected graph on n vertices with the independence number at most ⌈n/2⌉ and such that the degree sum of any pair of non-adjacent vertices is at least n − 3, then G is arbitrarily vertex decomposable. We present another result for connected graphs satisfying a similar condition, where the bound n − 3 is replaced by n − 2.

Cite this paper

@inproceedings{Mathematica2006AntoniMA, title={Antoni Marczyk A NOTE ON ARBITRARILY VERTEX DECOMPOSABLE GRAPHS}, author={Opuscula Mathematica}, year={2006} }