All week one lectures will be given in the first floor auditorium.
Given a family of sets, associate a vertex to each set and declare two
vertices adjacent if and only their corresponding sets have a non-empty
intersection. The resulting graph is called an intersection graph. When
restrictions are placed on the sets, many intriguing results can be
obtained which often have significant applications. For example, when the
sets are intervals the resulting intersection graph is called an interval
graph and has found applications in molecular biology. When the sets are
certain convex sets in the plane determined by points and their proximity
to each other, resulting intersection graphs have proven useful in pattern
recognition and data analysis. When the sets are subtrees of a tree, the
resulting intersection graph is called a chordal graph and has been an
important tool in evolutionary history estimation; etc. When conditions
are also placed on the "amount" of intersection of the sets, one obtains
tolerance intersection graphs. These graphs too have interesting
mathematical properties as well as applications to problems of society.