For more information about this meeting, contact Mary Anne Raymond.

Title: | Enumeration of the degree sequences of non-separable graphs and connected graphs |

Seminar: | Combinatorics/Partitions Seminar |

Speaker: | Dr. James Sellers, Department of Mathematics, The Pennsylvania State University |

Abstract: |

In 1962, S. L. Hakimi proved necessary and sufficient
conditions for a given sequence of positive integers d_1, d_2, ..., d_n
to be the degree sequence of a non-separable graph or that of a
connected graph. Our goal in this talk is to utilize Hakimi's results
to provide generating functions for the functions d_{ns}(2m) and
d_c(2m), the number of degree sequences with degree sum 2m representable
by non-separable graphs and connected graphs (respectively). From these
generating functions, we prove nice formulas for d_{ns}(2m) and d_c(2m)
which are simple linear combinations of the values of p(j), the number
of integer partitions of j. The proofs are elementary and the talk will
be accessible to a wide audience.
This is joint work with Oystein Rodseth and Helge Tverberg, both from the University of Bergen, Norway. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 09 / 02 / 2008 |

Time: | 11:15am - 12:05pm |