Tag Archives: clique number

The enhanced power graph is weakly perfect

Posted on 22/08/2022 by Peter Cameron

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 →

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Graphs on groups, 11

Posted on 02/01/2022 by Peter Cameron

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 →

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A new constant?

Posted on 23/05/2021 by Peter Cameron

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 | Tagged , , | 8 Comments

Graphs on groups, 4

Posted on 18/02/2021 by Peter Cameron

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 →

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The power graph yet again

Posted on 15/03/2016 by Peter Cameron

Five years ago, I posted a short update on the power graph of a group. Now, finally, the paper resulting from this has appeared on the arXiv; my coauthors are Ghodratollah Aalipour, Saieed Akbari, Reza Nikandish and Farzad Shaveisi. I … Continue reading →

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9,21,27,45,81,153,…

Posted on 16/10/2014 by Peter Cameron

This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. You could argue that the sequence should start with 3, … Continue reading →

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