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The tree packing conjecture for trees of almost linear maximum degree

2021/06/22 by Peter Allen, Julia Böttcher, Allen, Peter +9
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2106.11720

Abstract

We prove that there is c>0 such that for all sufficiently large n, if T1,…,Tn are any trees such that Ti has i vertices and maximum degree at most cn/log n, then \T1,…,Tn\ packs into Kn. Our main result actually allows to replace the host graph Kn by an arbitrary quasirandom graph, and to generalize from trees to graphs of bounded degeneracy that are rich in bare paths, contain some odd degree vertices, and only satisfy much less stringent restrictions on their number of vertices.

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