EN
Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge.
In this paper, we propose the following conjecture:
Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ.
This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.