ex8
Oirat Muktar
March 2026
1
Counterexample
Consider a connected, undirected graph with four vertices V = {A, B, C, D}
and the following five distinct edge weights:
4
A
B
9
C
1.1
6
8
11
D
Explanation
The unique Minimum weight spanning tree in this example uses edges [(A,B),
(B,C), (C,D)], but a Minimum cost paths rooted at any vertex will be forced
to use either the shortcut edge (A,C) or (B,D) to achieve lower cost of travel,
proving no such vertex v exists
1
0
