| ABSTRACT: |
This talk is about some combinatorial problems
that
arose in the study of phylogenetics.
Buneman introduced a special graph called a Buneman graph to prove
Splits-Equivalence Theorem by defining the vertices and edges in a
particular
way. As a natural generalization of trees and hypercubes, Buneman
graphs have close connection to the study of evolutionary relationships
within
populations.
In general, it is not easy to compute the number of vertices and the
number of maximal subcubes of a Buneman graph, which are two simple
measures of
complexity of a given graph.
In this talk I will present a special family of Buneman graphs and show
a combinatorial way for computing these measures.
This is joint work with K.T.Huber, J.H.Koolen, Y.S.Kwon, and V.Moulton. |