Complete Immersions In Graphs With Independence Number Two And Small Forbidden Subgraphs

The analogue of Hadwiger's conjecture for the immersion order states that every graph G contains the complete graph KX(G) as an immersion. Like its minor-order counterpart it is open even for graphs with independence number 2. Let G and H be graphs with independence number at most 2, such that |V(H)| ≤ 4. We show that if G is H-free, then G satisfies the conjecture.