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main.tex

@@ -226,6 +226,11 @@ It would be nice if we can characterize good parts in rigidity matroids with 1-t
 
 \section{Greedy base packing}
 
+\section{Principal sequence + KT contraction}
+
+Recently, Mohit Daga \cite{Daga_2025} combines the principal sequence of partitions and Kawarabayashi-Thorup contractions to get a sub-$n^k$ deterministic algorithm for $k$-cut in simple unweighted graphs.
+
+Recall that in the ideal tree packing framework \cite{Thorup_2008}, one finds the first partition with $\geq k$ parts in the principal sequence and then merge parts to get a bound. However, the idea in \cite{Daga_2025} is that, instead of finding the first partition with $\geq k$ parts, one finds the last partition $P$ with $<k$ parts and show that the optimal $k$-cut can be expressed as the $E[G/P]$ together with some internal cuts and some singleton isolations inside parts of $P$.
 
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