An Ore-type analogue of the Sauer-Spencer Theorem

Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer proved that if ∆(G1)∆(G2) < 0.5n, then G1 and G2 pack. In this note, we study an Ore-type analogue of the Sauer–Spencer Theorem. Let θ(G) = max{d(u) + d(v) : uv ∈ E(G)}. We show that if θ(G1)∆(G2) < n, then G1 and G2 pack. We also characterize the pairs (G1, G2) of n-vertex graphs satisfying θ(G1)∆(G2) = n that do not pack.

• Type: Journal
• Year: 2007
• Where: GC
• Authors: Alexandr V. Kostochka, Gexin Yu
• Keywords: Applied Computing, GC 2007, Injective Mappings, Ore-type Analogue, Sauer–Spencer Theorem