Topics in Graph Theory

Graph Theory is an area of modern mathematics with many applications in today’s world, but its roots lie in several recreational puzzles going back to the mid-eighteenth century. This chapter will introduce a few main topics in Graph Theory, drawing upon this history. The first two sections look at ways one can traverse a graph (Eulerian trails and Hamiltonian paths), while the last two sections deal with planar graphs (ones that can be drawn so their edges don’t cross) and graph coloring (graphs whose adjacent vertices have different colors). While connected to a couple of earlier topics, this concluding chapter has a more geometric character, balancing out the algebraic emphasis of the rest of the text.