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hw5: Fix hint
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Lipen committed Mar 31, 2024
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\item Consider a graph of subway lines in Saint Petersburg in 2050\Href{https://web.archive.org/web/20240301072159/https://commons.wikimedia.org/wiki/File:Saint_Petersburg_metro_future_map_RUS.png}.
Represent each transfer station as a single vertex.
Smoothen out\Href{https://en.wikipedia.org/wiki/Homeomorphism_(graph_theory)\#Subdivision_and_smoothing} all 2-degree vertices and remove all pendant (1-degree) vertices (\emph{repeat until fixed point}).
In the resulting graph\footnote{Hint: the resulting subway graph consists of 28 vertices (transfer stations).}, find vertex and edge connectivity, maximum stable set, maximum matching, minimum dominating set, minimum vertex and edge covers.
In the resulting graph\footnote{Hint: the resulting subway graph consists of 29 vertices (transfer stations).}, find vertex and edge connectivity, maximum stable set, maximum matching, minimum dominating set, minimum vertex and edge covers.


\item Find an error in the following inductive \enquote{proof} of the statement that every tree with $n$ vertices has a path of length $n - 1$.
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