October 13
Vincent Guingona,
Towson University
Indivisibility of Classes of Graphs
This talk will discuss my work with Miriam Parnes and four undergraduates which took place last summer at an REU at Towson University. We say that a class of structures in some fixed language is indivisible if, for all structures A in the class and number of colors k, there is a structure B in the class such that, no matter how we color B with k colors, there is a monochromatic copy of A in B. Parnes and I became interested in this property when studying the classification of theories via positive combinatorial configurations. In this talk, following the work with our students, I will examine indivisibility on classes of graphs. In particular, we will look at hereditarily sparse graphs, cographs, perfect graphs, threshold graphs, and a few other classes. This work is joint with Felix Nusbaum, Zain Padamsee, Miriam Parnes, Christian Pippin, and Ava Zinman.