## The Mycielskian of a Graph

Let ω(*G*) and χ(*G*) be the clique number and the chromatic number of a graph *G*. Mycielski [11] presented a construction that for any *n* creates a graph *M _{n}* which is triangle-free (ω(

*G*) = 2) with χ(

*G*) >

*n*. The starting point is the complete graph of two vertices (

*K*

_{2}).

*M*(

_{n+1}) is obtained from

*M*through the operation μ(

_{n}*G*) called the Mycielskian of a graph

*G*.

We first define the operation μ(*G*) and then show that ω(μ(*G*)) = ω(*G*) and χ(μ(*G*)) = χ(*G*) + 1. This is done for arbitrary graph *G*, see also [10]. Then we define the sequence of graphs *M _{n}* each of exponential size in

*n*and give their clique and chromatic numbers.