Contents Online

# Journal of Combinatorics

## Volume 1 (2010)

### Number 2

### The saturation function of complete partite graphs

Pages: 149 – 170

DOI: http://dx.doi.org/10.4310/JOC.2010.v1.n2.a5

#### Authors

#### Abstract

A graph $G$ is called \emph{$F$-saturated} if it is $F$-free but theaddition of any missing edge to $G$ creates a copy of $F$.Let the saturation function $\sat(n,F)$ be the minimum numberof edges that an $F$-saturated graph on $n$ vertices can have.We determine this function asymptotically forevery fixed complete partite graph $F$ as $n$ tends to infinity andgive some structural information aboutalmost extremal $F$-saturated graphs.If the two largest parts of $F$ have different sizes,then we can reduce the error term to an additive constant.