Deviation estimates for Eulerian edit numbers of random graphs

Abstract

Consider the random graph G(n,p) obtained by allowing each edge in the complete graph on n vertices to be present with probability p independent of the other edges. In this paper, we study the minimum number of edge edit operations needed to convert G(n,p) into an Eulerian graph. We obtain deviation estimates for three types Eulerian edit numbers based on whether we perform only edge additions or only edge deletions or a combination of both and show that with high probability, roughly n4 operations suffice in all three cases.