On a packing problem of Alon and Yuster
نویسندگان
چکیده
Two graphs G1 and G2, each on n vertices, pack if there exists a bijection f from V (G1) onto V (G2) such that uv ∈ E(G1) only if f (u)f (v) ∉ E(G2). In 2014, Alon and Yuster proved that, for sufficiently large n, if |E(G1)| < n − δ(G2) and ∆(G2) ≤ √ n/200, then G1 and G2 pack. In this paper, we characterize the pairs of graphs for which the theorem of Alon and Yuster is sharp.We also prove the stronger result that for sufficiently large n, if |E(G1)| ≤ n, ∆(G2) ≤ √ n/60, and ∆(G1) + δ(G2) ≤ n − 1, then G1 and G2 pack whenever there is a vertex v1 ∈ V (G1) such that d(v1) = ∆(G1) and α(G1 − N[v1]) ≥ δ(G2). © 2016 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 339 شماره
صفحات -
تاریخ انتشار 2016