Dear all,
There will be a noon seminar this Thursday, 28 March, given by Todor Antić. Please find the talk details below.
Best regards, Misha Tyomkyn.
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Star-Forest Decompositions of Complete (Geometric) Graphs Todor Antić Charles University March 28, 2024, 12:20 in S6
Abstract A star-forest is a forest in which every component is a star. A plane star-forest is a star-forest drawn in the plane with no crossings. We deal with the problem of decomposing Complete (Geometric) Graphs into (plane) star-forests. In the Abstract case, it is known that $K_n$ can be decomposed into $\lceil \frac{n}{2}\rceil+1 $ star-forests and that this is is thight. We show that for even $n$, any such forest is "unique" in a certain sense. We also construct Complete Geometric Graphs on $n$ vertices which can be decomposed into $\lceil \frac{n}{2}\rceil +1$ plane star-forests, resolving the conjecture of Pach, Saghafian and Schnider.
This is joint work with Milan Milivojčević and Jelena Glišić
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