A note on arbitrarily vertex decomposable graphs

A note on arbitrarily vertex decomposable graphs

Blog Article

A graph (G) of order (n) is said to be arbitrarily vertex decomposable if for each sequence ((n_{1},ldots,n_k)) of positive integers such that (n_{1}+ldots+n_{k}=n) there exists a partition ((V_{1},ldots,V_{k})) of the vertex set of a&d ej-123 (G) such that for each (i in {1,ldots,k}), (V_{i}) induces a connected subgraph of (G) on (n_i) vertices.In this paper we show that if (G) is a vegas golden knights background two-connected graph on (n) vertices with the independence number at most (lceil n/2
ceil) 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).