Unformatted text preview: not list all the characteristics that you can think of, but rather describe in a few sentences the necessary and sufﬁcient properties of such graphs. Question 5 (Spanning Graphs, 3 points) . Let G = ( V , E ) be a connected, undirected graph. We say that H is a “spanning graph” of G if and only if H = ( V , F ) is also a connected, undirected graph, with F ⊆ E . Prove that the smallest possible spanning graph, i.e. the one with the smallest possible set of edges F , will always be a tree. Note: this question tries to test your skills in interpreting by yourself new deﬁnitions (like the one here for spanning graphs). As a result, the TA (PK) and I (WvD) will not help you with this speciﬁc exercise....
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 Fall '09
 Egiceoclu
 Equivalence relation, Binary relation, undirected graph, Total order, one bit, equivalences

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