Elsevier

Discrete Mathematics

Volume 339, Issue 8, 6 August 2016, Pages 2178-2185
Discrete Mathematics

A list version of graph packing

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Abstract

We consider the following generalization of graph packing. Let G1=(V1,E1) and G2=(V2,E2) be graphs of order n and G3=(V1V2,E3) a bipartite graph. A bijection f from V1 onto V2 is a list packing of the triple (G1,G2,G3) if uvE1 implies f(u)f(v)E2 and for all vV1, vf(v)E3. We extend the classical results of Sauer and Spencer and Bollobás and Eldridge on packing of graphs with small sizes or maximum degrees to the setting of list packing. In particular, we extend the well-known Bollobás–Eldridge Theorem, proving that if Δ(G1)n2,Δ(G2)n2,Δ(G3)n1, and |E1|+|E2|+|E3|2n3, then either (G1,G2,G3) packs or is one of 7 possible exceptions.

Keywords

Graph packing
Maximum degree
Edge sum
List coloring

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