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 leastΩ((d/ log d)1/3). This settles a problem of Havet, Klazar, Kratochvil, Kratsch and Liedloff.
Dedication
This paper is dedicated to Laci Lovász, for his 60th birthday. It settles a problem presented by Jan Kratochvil at the open problems session of the meeting Building Bridges, which took place in Budapest in August 2008, celebrating this birthday. The Lovász Local Lemma is applied extensively throughout the proof. This work is therefore a typical example illustrating the immense influence of Laci, who not only provided the community with powerful tools and techniques, but also stimulated research by his books, lectures and organization of conferences.
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© 2010 János Bolyai Mathematical Society and Springer-Verlag
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Alon, N., Wormald, N. (2010). High Degree Graphs Contain Large-Star Factors. In: Katona, G.O.H., Schrijver, A., Szőnyi, T., Sági, G. (eds) Fete of Combinatorics and Computer Science. Bolyai Society Mathematical Studies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13580-4_1
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