## Graph Theory

### Announcements

Don't Forget About The Written Project!

Extra Credit opportunities can be found here
### Additional Homework

Graph Homework #1--Due: Tuesday April 21

Graph Homework #2--Due: Tuesday April 28
### Course Materials

Review Sheet

Review Sheet---Solutions

Graph Homework #1--Solutions

### Class Slides

Here are the Graph Theory Slides. They are not divided up by day, so I will make a note here for which slides were covered each day.

##### April 14th Material

We covered Slides 1-22. (i.e Slide Titled ``New Topic" to the Slide Titled ``Graph Isomorphism") That is, we covered the basic definitions, the 2 theorems on Graph Isomorphisms, and began talking about how to show graph isomorphisms explicitly.
##### April 16th Material

We covered Slides 22-40. (i.e Slide Titled ``Graph Isomorphism" to the Slide Titled ``Counting Faces and Degrees 2"), however we skipped slides 29 & 30 (i.e. ``Compare with a Neighbor 1 & 2"). We covered how to find graph isomorphisms in more detail, we defined planar graphs, faces, degree of faces, and eluded heavily to (although not yet defining) Euler's Formula.
##### April 21st Material

We covered Slides 41-65. (i.e Slide titled ``Counting Faces and Degrees 3" to the slide titled ``Vertex Coloring 8"). Specifically, we covered Euler's Formula (connected planar graphs), Euler's General Formula (planar graphs), the basics of vertex coloring, Chromatic number 1 theorem, chromatic number 2 theorem, and the Four Color Theorem.
##### April 23rd Material

Due to the MiniExam and Course Evaluations, we only covered Slides 64-73. We covered a little more on graph coloring before moving on to Modeling with Graphs, specifically the scheduling problems.

##### April 28th Material

We covered Slides 73-110. (It was not as much as it sounds like.) We covered modeling maps with graphs, Eulerian Circuits, Eulerian Paths, Eutherian Graphs, Semi-Eulerian Graphs, and associated theorems.
##### April 30th Material

We covered Slides 111-119. We talked about Eulerizing graphs. Additionally, we reviewed for the Final Exam.

.