[Colloquium] Reminder: Mirsattari/MS Presentation/Feb 15, 2011

[Margaret Jaffey]

This is a reminder about Negar's MS Presentation tomorrow.

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Date:  Tuesday, February 15, 2011

Time:  9:00 AM

Place:  Ryerson 277

M.S. Candidate:  Negarsadat Mirsattari

M.S. Paper Title: Properties of Degree Sequences of k-Uniform
Hypergraphs

Abstract:
A "k-uniform hypergraph" H is a pair H = (V,E), where V is a set of
elements, each called a "vertex", and E = {S_1, S_2, ..., S_m } is a
collection of distinct k-subsets of V, each called a "hyperedge". The
"degree" of a vertex v, denoted by deg(v), is equal to the number of
(hyper)edges incident with the vertex v. The "degree sequence" of a
(hyper)graph H with vertices v_1, v_2,..., v_n is defined as
d(H)=(deg(v_1), deg(v_2), ..., deg(v_n) ).

The problem of characterizing degree sequences of k-uniform
hypergraphs, i.e. k-hypergraphic sequences, is a long standing open
question in hypergraph theory. We investigate properties of degree
sequences of k-hypergraphs as well as the properties of their convex
hull polytopes. We introduce a set of necessary conditions on a
non-negative integral sequence to be k-hypergraphic, dividing vertices
and hyperedges into distinct classes.

For properties of the convex hull polytopes of k-hypergraphic
sequences, first we generalize some known properties of the polytopes
of (simple) graphical sequences to the polytope of k-hypergraphic
sequences, using our result for properties of k-hypergraphical
sequences. Then we reduce an open problem concerning "holes" in the
polytope of degree sequences to a well-known problem on lattice
points.

Negarsadat's advisors are Prof. Janos Simon and Prof. Caroline Klivans

Login to the Computer Science Department website for details:
 https://www.cs.uchicago.edu/phd/ms_announcements#mirsattari

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Margaret P. Jaffey            margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 156)               (773) 702-6011
The University of Chicago      http://www.cs.uchicago.edu
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