# Math 442 Assignments

### General remarks

1. Homework should be legible and neat, questions should be answered in order, and pages should be fastened with a staple with your name and student number on at least the front page in pen.

2.
3. Homework will be collected on Thursdays at the start of class and will cover the material through Tuesday's lecture (roughly). You should start attempting the problems as soon as possible after the material is presented in lecture. Please don't save it all for Wednesday night.

4.
5. Solutions should be written carefully, using good English, complete sentences, and full details, with citations from the notes or homework. Some of these solutions will be explanatory proofs. A good guideline here is that you should write proofs the way you would like to see them in your textbook, and with as much detail as the class notes including all the verbal descriptions. In summary,  show all your working to get full marks.

#### Assignment 1, due Thursday, January 4th

Covering proof techniques frequently needed for the course

Problems 1, 2, 3, 4, 5, 6

#### Assignment 2, due Thursday, January 11th

Covering classical problems

Problems 7, 8, 9, 10, 11, 12

#### Assignment 3, due Thursday, January 18th

Covering basic theory, complement, isomorphism, representations and types of graphs

Problems 13, 14, 15, 16, 17, 18

#### Assignment 4, due Thursday, January 25th

Covering Eulerian and Hamiltonian graphs, and applications

Problems 19, 20, 21, 22, 23, 24

#### Assignment 5 due Thursday, February 1st

Covering planarity, Euler's Theorem and inequalities

Problems  25, 26, 27, 28, 29, 30

#### Assignment 6 due Thursday, February 15th

Covering polyhedra, duals and line graphs

Problems 31, 32, 33, 34, 35, 36

#### Assignment 7, due Thursday, March 1st

Covering colouring, the chromatic polynomial and number, deletion-contraction

Problems 37, 38, 39, 40, 41, 42

#### Assignment 8, due Thursday, March 8th

Covering the five colour theorem, face colouring, edge colouring

Problems   43, 44, 45, 46, 47, 48

#### Assignment 9, due Thursday, March 15th

Covering scheduling problems, classical results on trees

Problems  49, 50, 51, 52, 53, 54

#### Assignment 10, due Thursday, March 22nd

Covering spanning trees, Prufer sequences

Problems 55, 56, 57, 58, 59, 60

#### Assignment 11, due Thursday, March 29th

Covering BFS and DFS, shortest paths, minimal spanning trees

Problems 61, 62, 63, 64, 65, 66

#### Assignment 12, due Thursday, April 5th

Covering TSP, digraphs, max flow-min cut

Problems 67, 68, 69, 70, 71, 72