The Pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is True

We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Grout, Logan, Moore, Benjamin
Format: Article
Language:English
Subjects:
Integers
Online Access:Get full text
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Summary:We prove that for any positive integers \(k\) and \(d\), if a graph \(G\) has maximum average degree at most \(2k + \frac{2d}{d+k+1}\), then \(G\) decomposes into \(k+1\) pseudoforests \(C_{1},\ldots,C_{k+1}\) such that there is an \(i\) such that for every connected component \(C\) of \(C_{i}\), we have that \(e(C) \leq d\).
ISSN:2331-8422