3 p.m. - 4 p.m. Location: SLC 1.202
University of Illinois at Urbana-Champaign
Factors in graphs
A factor is a subgraph that includes every vertex of its host graph. For example, a perfect matching is a factor consisting entirely of disjoint edges and a Hamiltonian cycle is a factor that is a cycle. Many important classical results in graph theory give sufficient conditions for the existence of a specified factor. For instance, in 1952 Dirac proved that if every vertex in a graph with at least three vertices is adjacent to at least half of the vertices, then the graph contains a Hamiltonian cycle. In this talk, we will discuss extensions and generalizations of classical results similar to Dirac's Theorem.
Sponsored by the Department of Mathematical Sciences