Neighbourhood and Degree Conditions for the Existence of Regular Factors

Ursula Lenkewitz1, Lutz Volkmann1
1Lehrstuhl I fir Mathematik, RWTH Aachen, 52056 Aachen, Germany

Abstract

We present sufficient conditions for the existence of a \(k\)-factor in a simple graph depending on \(\sigma_2(G)\) and the neighbourhood of independent sets in our first theorem and on \(\sigma_2(G)\) and \(\alpha(G)\) in the second one.