MATH 2602 Homework #12-#15
Due Wednesday Nov 14 - Dec 3, covering the material of the Final Exam
- Homework 12 - Due Nov 12 [Barone-Celaya-McKay]
- Core : Book problems: Section 10.1 on page 309 problems 1, 3, 4bf, 11, 12, 13, 15, 16, 17, 18, 21, 23.
Also this problem :
Show that the book's definition of connectedness agrees with the definition given in class. That is, show that the two definitions
below are logically equivalent.
Definition 1 (from class): A graph G=(V,E) is disconnected if there exist non-empty
subgraphs H1=(V1,E1) and H2=(V2,E2) such that V1 and V2
partition V and E1 and E2 partition E.
A graph is connected if it is not disconnected.
Definition 2 (from book): A graph G is connected if for any two vertices v,w there is a walk between v and w.
- Supplementary: None.
- Homework 13 - Due Nov 19 [Barone-McKay-Rybka]
- Core : Book problems: Section 10.2 on page 317 problems: 1, 3, 5.
Section 10.3 on page 324 problems: True and False problems 1-10, and problems 7, 8 on page 325.
Section 11.2 on page 350 problems: 1, 2.
Section 13.1 on page 417 problems: 1, 2.
- Supplementary: None.
- Homework 14 - Due Nov 26 [Barone-Rybka-Kim]
- Core : Book problems: Section 13.2 on page 425 problems: 4, 7, 8.
Section 13.1 on page 417 problems: 4, 5.
Section 12.2 on page 283 problems: 2, 8.
Extra problem: Consider problem 7 of Section 13.2 on page 425. In part (a) you explain why a a tree is planar.
Then in part (b) you explain how you can conclude that since a tree is planar, and V-E+R=2 for
planar graphs (and R=1 for trees), that E=V-1. Why is this logic flawed?
Or rather, why should part (a) and part (b) bother you?
(Hint: go back to the proof of Euler's Theorem, that V-E+R=2 for planar graphs)
- Supplementary: None.
- Homework 15 - Due Dec 3 [Barone-Kim-Celaya] The week before finals
- Core : Book problems: CANCELLED. For the final it is suggested that you be able to do problems like number 1a-d (parts i and ii) on page 448 in Section 14.2.
- Supplementary: None.
- Final Exam will cover material from Hw 1-15.