For Mon. 1/26: Read Sections 1.1, 1.2.

Do for discussion Thurs. 1/29:

Sect. 1.1, ## 1, 2, 4(a-c), 6, 9(a).

Sect. 1.2, # 1, 5, 7, 8.

# B3(a).

Do for discussion Fri. 1/30:

Sect. 1.2, ## 2, 3.

## B1, B2, B3(b).

Hand in Mon. 2/2:

Sect. 1.1, ## 3, 4(d), 5, 7, 8, 9(b).

Sect. 1.2, ## 4, 6.

# B4.

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B1. This concerns Theorem 1.1.2 and the example G_{0}. I'll follow the book's notation. **NOTE: There are some errors in this question. The corrected version is Problem # BB1 in HW Set IIa.)**
The sequence

(S1) (4, 4, 4, 3, 3, 3, 2, 2, 1)

is known to be graphic, because it is the degree sequence of G_{0}. From (S1) the rule of Theorem 1.1.2 gives

(S2) (3,3,2,2,3,2,2,1).

- (a) In this example what are s, t
_{1}, ..., t_{s}, n, d_{1}, ..., d_{n}? (Give their values.) - (b) Label the vertices of G
_{0}by S, T_{1}, ..., T_{s}, D_{1}, ..., D_{n}as in the proof of the theorem. (Note: Do*not*choose S = h.) - (c) If you delete vertex S, does the new graph G
_{0}- S have (S2) as its degree sequence? - (d) Use
*the method in the proof*to modify G_{0}so that, when you delete S, you do get (S2) as the degree sequence of the new graph.

B2. In which graphs is the whole vertex set V the only separating set?

B3. In G_{2} from Homework I, find the values of (a) kappa(1, 5), (b) kappa(2, 6). Use Menger's Vertex Theorem to prove you are correct: i.e., find the internally disjoint paths that the theorem tells us exist.

B4. The same as B3, but for kappa(v_{3}, v_{5}) in G_{3} from Homework I.