| Speaker: Professor Paul Gartside Affiliation: University of Pittsburgh Time: 2 pm Thursday, 30 May, 2019 Location: 303-G15 |
| Two foundational problems in graph theory concern paths. Euler's Problem is to characterize the graphs with a path crossing every edge exactly once. Hamilton's problem is to determine which graphs have a path visiting every vertex exactly once. Traditionally graphs are considered from an abstract and combinatorial perspective - a graph is a set of vertices along with a set of pairs of vertices (the edges), and a path in a graph is a special type of sequence of edges. But every graph is also, very naturally, a topological space. The one you visualize when you draw a graph: points for vertices and arcs for edges. And paths are, well, paths. In this talk we will consider paths in graphs considered as spaces. We will also consider how known results about (combinatorial) paths in graphs can be extended to more general spaces, particularly continua (compact, connected metric spaces). |