For Fri. 3/4 and Mon. 3/7 Tues. 3/8: Read Sect. 3.1, including the proofs.
Do for discussion Tues. 3/8 Wed. 3/9:
Sect. 2.3, ## 17.
Sect. 2.4, ## 3, 10.
Sect. 3.1, ## 1-3, 4 (for Q3, I, K4,4 only), 7, 11.
Do for discussion Wed. 3/9 Fri. 3/11:
Sect. 2.4, ## 9 (Fig. 2.3.7), 12, 21.
Sect. 3.1, ## 5, 8, 13, 14.
## G1(a), G2(a), G3, G4.
Hand in Fri. 3/11 Mon. 3/14:
Sect. 2.4, # 22.
Sect. 3.1, ## 6, 12, 15, 16.
## G1(b, c), G2(b, c), G3(b).
See the corrections for Section 3.1.
G1. Decompose into the fewest possible trails:
(a) Fig. 1.2.3 (left).
(b) Fig. 2.1.9.
(c) Fig. 2.2.6 (right).
G2. Decompose into the fewest possible paths: (a, b, c) from #G1.
G3. Decide whether the graph is Hamiltonian (i.e., has a Hamilton cycle):
(a) Fig. 2.1.3.
(b) Fig. 2.4.1, the Petersen graph.
G4. Verify that, in the proof of Theorem 2.3.2, the first two 1-factors unite to form a Hamilton cycle. Your proof should be valid for all n ≥ 2.