Embedding induced trees in sparse expanding graphs
Inspired by the network routing literature \cite{aggarwal1996efficient}, we develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree induced trees in sparse expanders. This generalises a powerful and central result of Friedman and Pippenger to the induced setting. As corol...
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| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
06.06.2024
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| Online Access | Get full text |
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| Abstract | Inspired by the network routing literature \cite{aggarwal1996efficient}, we
develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree
induced trees in sparse expanders.
This generalises a powerful and central result of Friedman and Pippenger to
the induced setting.
As corollaries we obtain that a sparse random graph contains all bounded
degree trees of linear order (whp) and that the induced and size induced Ramsey
numbers of bounded degree trees are linear. No such linear bounds were
previously known. We also prove a nearly-tight result on induced forests in
bounded degree countable expanders. We expect that our new result will find
many more applications. |
|---|---|
| AbstractList | Inspired by the network routing literature \cite{aggarwal1996efficient}, we
develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree
induced trees in sparse expanders.
This generalises a powerful and central result of Friedman and Pippenger to
the induced setting.
As corollaries we obtain that a sparse random graph contains all bounded
degree trees of linear order (whp) and that the induced and size induced Ramsey
numbers of bounded degree trees are linear. No such linear bounds were
previously known. We also prove a nearly-tight result on induced forests in
bounded degree countable expanders. We expect that our new result will find
many more applications. |
| Author | Girão, António Hurley, Eoin |
| Author_xml | – sequence: 1 givenname: António surname: Girão fullname: Girão, António – sequence: 2 givenname: Eoin surname: Hurley fullname: Hurley, Eoin |
| BackLink | https://doi.org/10.48550/arXiv.2406.04260$$DView paper in arXiv |
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| Snippet | Inspired by the network routing literature \cite{aggarwal1996efficient}, we
develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree... |
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| Title | Embedding induced trees in sparse expanding graphs |
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