Perfectly packing graphs with bounded degeneracy and many leaves
Allen, Peter
; Böttcher, Julia; Clemens, Dennis; and Taraz, Anusch
Perfectly packing graphs with bounded degeneracy and many leaves.
Israel Journal of Mathematics.
ISSN 0021-2172
; Böttcher, Julia; Clemens, Dennis; and Taraz, Anusch
Perfectly packing graphs with bounded degeneracy and many leaves.
Israel Journal of Mathematics.
ISSN 0021-2172
We prove that one can perfectly pack degenerate graphs into complete or dense n-vertex quasirandom graphs, provided that all the degenerate graphs have maximum degree(Formula Presented.)., and in addition Ω(n) of them have at most (1 − Ω(1))n vertices and Ω(n) leaves. This proves Ringel’s conjecture and the Gyárfás Tree Packing Conjecture for all but an exponentially small fraction of trees (or sequences of trees, respectively).
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