Lovász theta

Lovász theta is like a special way of measuring how well a graph can be colored. A graph is like a bunch of dots (called "vertices") connected by lines (called "edges"). People who study graphs like to color the vertices so that no two vertices that are connected have the same color. This is called a "proper coloring."

The Lovász theta number tells you how many colors you need to properly color a graph. The number is always between 1 and the number of vertices in the graph. The bigger the number, the harder the graph is to color.

Mathematicians use some special tricks to figure out the Lovász theta number. One trick involves using a special matrix called the "adjacency matrix," which is like a big table showing which vertices are connected by edges. Another trick involves using something called a "semidefinite program," which is a special way of solving certain types of mathematical problems.

So, in summary, Lovász theta is a special number that tells you how hard it is to color a graph. It's found using fancy mathematical methods involving matrices and semidefinite programs.