Constructions for large sets of disjoint compatible packings on 6k+5 points

Abstract

In this paper, we give two methods to construct large sets of disjoint compatible packings (LMP(1^vC₄)) on 6k+5 points. As a result, we prove that there exists an (LMP(1^vC₄)) for v=7ⁱ u^j where i ≥ 0, j ≥ 1 and u ∈ {13, 19, 25, 31, 43, 67, 139, 163, 211, 283, 307, 331, 379}.