# Assaf Rinot: The fragility of chromatic number of graphs

07/Jun/2013, 13:30–15:00
Fields institute,Room 230

Speaker: Assaf Rinot

Title: The fragility of chromatic number of graphs

Abstract: The chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a coloring $c:G\rightarrow\kappa$ with the property that $c(x)\neq c(y)$ whenever $xEy$. How robust is this notion? Could a graph change its chromatic number via forcing? via a cofinality-preserving forcing? Could the same graph have different chromatic numbers in different cofinality-preserving forcing extensions? and if so, is there a bound for the amount of different chromatic numbers the same graph can get? and what is the effect of forcing axioms on this problem?

In this talk, we shall address all of these questions.