# MAT4323

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## Catalog entry

*Prerequisite*: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

*Contents*

Graph models (Isomorphisms, edge counting, planar graphs), Covering circuits and graph colorings (Euler circuits, Hamilton circuits, graph colorings), Network algorithms (Shortest path, minimum spanning trees, matching algorithms, transportation problems), Ramsey's Theorem and Ramsey numbers.

## Sample textbooks

[1] Vladlen Koltun, *Discrete Structures, Lecture Notes, Stanford University*, 2008. Freely available online here

[2] Alan Tucker, *Applied Combinatorics*, Freely available online here

[3] Gary Chartrand and Ping Zhang, *A First Course in Graph Theory*, Dover Books on Mathematics, 2012.

## Topics List

Week | Topic | Sections from Tucker's book | Subtopics | Prerequisite |
---|---|---|---|---|

1-3 | Graph models | 12.1-12.3 | Isomorphism, edge counting, planar graphs. | |

4-6 | Covering circuits | 2.1-2.4 | Euler circuits, Hamilton circuits, graph colorings, coloring theorems. | |

8-9 | Trees | 3.1-3.4 | Search trees, spanning trees, the Traveling Salesman Problem | |

10-12 | Network algorithms | 4.1-4.5 | Shortest path , minimum spanning trees, matching algorithms, transportation problems. | |

13-14 | Finding order within chaos | Ramsey's Theorem and Ramsey numbers |