# Tag Archives: clique number

## The enhanced power graph is weakly perfect

Earlier this year, I posed a combinatorial problem, a solution to which would imply that, for any finite group G, the enhanced power graph of G is weakly perfect, that is, has clique number equal to chromatic number. Recall that … Continue reading

Posted in doing mathematics | | 19 Comments

## Graphs on groups, 11

A brief interlude to describe another recent preprint, and as in the preceding post I will concentrate on one result in the paper. I don’t know why it happens, but in this project one of the most interesting graph parameters … Continue reading

## A new constant?

This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading

Posted in doing mathematics, open problems | | 8 Comments

## Graphs on groups, 4

Here is a small problem, mixing group theory and number theory, which might appeal to someone. A couple of definitions. The power graph of a group G has an edge from x to y if one is a power of … Continue reading