From d963fbeaa9b2748916f0cabc8abbacf11ee2ce50 Mon Sep 17 00:00:00 2001
From: Konstantin Chukharev <lipen00@gmail.com>
Date: Tue, 5 Mar 2024 18:10:48 +0300
Subject: [PATCH] hw5: Change problem statement

---
 hw5.tex | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/hw5.tex b/hw5.tex
index 5fb6877..c180882 100644
--- a/hw5.tex
+++ b/hw5.tex
@@ -367,10 +367,8 @@
 
 
     \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}.
-    Consider only the vertices corresponding to transfer stations.
-    Smoothen out all other (non-transfer) vertices between transfer stations and also remove all pendant non-transfer vertices.
-    Denote the resulting graph~$G$.
-    Find~its vertex and edge connectivity, cut vertices and bridges, blocks and islands.
+    Smoothen out all vertices, i.e. retain only transfer and final stations.
+    Find all cut vertices and bridges, blocks and islands, maximum stable set, maximum matching, minimum dominating set, minimum vertex cover, minimum edge cover.
 
 
     \item Find an error in the following inductive \enquote{proof} of the statement that every tree with $n$ vertices has a path of length $n - 1$.