Abstract
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 Δ (G1) Δ (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)Δ(G2) < n, then G1 and G2 pack. We also characterize the pairs (G1,G2) of n-vertex graphs satisfying θ(G1)Δ(G2) = n that do not pack.
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This work was supported in part by NSF grant DMS-0400498. The work of the first author was also partly supported by grant 05-01-00816 of the Russian Foundation for Basic Research.
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Kostochka, A., Yu, G. An Ore-type analogue of the Sauer-Spencer Theorem. Graphs and Combinatorics 23, 419–424 (2007). https://doi.org/10.1007/s00373-007-0732-1
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DOI: https://doi.org/10.1007/s00373-007-0732-1