Colloquium Announcement
Department of Mathematics
West Virginia University

for

Thursday, October 22,1998, at 3:45pm in 315 Armstrong Hall

(Tea and cookies begin at 3:00 in coffee room.)

Professor Ronald J. Gould

Emory University


On the Structure of 2-Factors

The talk will be suitable for a general audience.

Students are strongly encouraged to participate.

Abstract


For a graph G with vertex set V and edge set E, we define a 2-factor to be 2-regular subgraph of a G, that is, it is the union of disjoint cycles that covers V. The case of a single cycle (hamiltonian cycle) in the 2-factor has been extensively studied. We consider the situation of more than one cycle, where considerable progress has been made in recent years. Several results which attempt to specify the exact structure (that is, number of cycles and length of each cycle) will be presented.

In addition, results using weaker conditions, that ask for the range of possibilities for the number of cycles composing the 2-factor will also be presented.

All the results depend on some type of edge density condition. Several such conditions will be explored, including the classic degree sum condition, toughness, and forbidden subgraphs.


The information on the future (and past) Colloquia can be also found on web at the address:

http://www.math.wvu.edu/homepages/kcies/colloquium.html