Graph decomposition with constraints on the connectivity and minimum degree

Abstract

Abstract For each pair s,t of natural numbers there exist natural numbers f(s,t) and g(s,t) such that the vertex set of each graph of connectivity at least f(s,t) (respectively minimum degree at least g(s,t)) has a decomposition into sets which induce subgraphs of connectivity (respectively minimum degree) at least s and t , respectively.