Biclique immersions in graphs with independence number 2

Abstract

The analogue of Hadwiger‘s Conjecture for the immersion relation states that every graph G contains an immersion of Kx(G). For graphs with independence number 2, this is equivalent to stating that every such n-vertex graph contains an immersion of K[n/2]. We show that every n-vertex graph with independence number 2 contains every complete bipartite graph on [n/2] vertices as an immersion.