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arXiv · 0810.2053

High degree graphs contain large-star factors

Noga Alon·Nicholas Wormald
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Abstract

We show that any finite simple graph with minimum degree $d$ contains a spanning star forest in which every connected component is of size at least $Ω((d/\log d)^{1/3})$. This settles a problem of J. Kratochvil.

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Noga Alon, Nicholas Wormald. 2008-10-11. High degree graphs contain large-star factors. https://arxiv.org/abs/0810.2053

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