Lunedì 7 Ottobre 2019 alle ore 14:30
Sala Conferenze "F. Tricerri" Dipartimento di Matematica e Informatica "U. Dini"
"On Null 3-Hypergraphs"
Prof. William Kocay
St. Paul's College
University of Manitoba
Canada
A label ±1 is assigned to the triples of a 3-hypergraph H, so that some triples are positive and some are negative.
The positive degree of any vertex v is d+(v), and the
negative degree is d-(v). If d+(v)-d-(v) = 0, for every
vertex v, the labelling is a null labelling and H is called
a null hypergraph. Given 3-hypergraphs H1 and H2 with the same degree
sequence, H1 can be transformed into H2 by a sequence of interchanges
using null hypergraphs on 5 and 6 vertices. We consider the
question of characterizing when a 3-hypergraph has a null labelling.
If H has n vertices, it appears that there is always a null labelling
if the number of triples is at least n(n-1)(n-2)/12.