Packing d-degenerate graphs

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Abstract

We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobás–Eldridge–Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d,Δ1,Δ21 and n>max{40Δ1lnΔ2,40dΔ2} then a d-degenerate graph of maximal degree Δ1 and a graph of order n and maximal degree Δ2 pack. We use this result to show that, for d fixed and n large enough, one can pack n1500d2 arbitrary d-degenerate n-vertex graphs of maximal degree at most n1000dlnn.

Keywords

Graph packing
d-Degenerate graphs
Maximum degree

Cited by (0)

1

Research supported by NSF grants CCR-0225610 and DMS-0505550.

2

Research supported by the NSF grants DMS-0099608 and DMS-0400498.