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Tag Archives: chromatic 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
Tagged chromatic number, clique number, enhanced power graph, Euler's totient
19 Comments
Why I’d like to see this solved
I am aware that quite a number of people have been captivated by the problem I posed. So here is the motivation for it, with some additional remarks and commennts. First, to repeat the problem: Problem: Let n be a … Continue reading
Posted in doing mathematics
Tagged chromatic number, enhanced power graph, GruenbergKegel graph
3 Comments
The power graph yet again
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
9,21,27,45,81,153,…
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