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 dsp on The enhanced power graph is weakly perfect
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Tag Archives: graphs
Graphs on groups, 3
Since this stuff keeps growing, I have decided to keep the most recent version on the web. It is now nearly twice as long as the first version I circulated. If you are interested, please take a copy: it’s at … Continue reading
G2D2, 1: setting the scene
I’m in Yichang, at the China Three Gorges University, for the conference and summer school G2D2 (“Groups and graphs, designs and dynamics”). This is the sixth meeting in the series: the previous ones were G2C2: Groups and graphs, cycles and … Continue reading
Posted in exposition, history, Uncategorized
Tagged designs, dynamics, G2 conferences, graphs, groups, Hangzhou, Three Gorges University, Yichan, Zhejiang University
1 Comment
OuLiPo
OuLiPo, or Ouvroir de Littérature Potentielle (which they translate as “Charity bazaar of potential literature”) were a collection of writers I knew little about until yesterday. I knew a couple of things: Martin Gardner wrote about them, mentioning among other … Continue reading
Posted in mathematics and ...
Tagged Claude Berge, combinations, games, Georges Perec, graphs, groups, literature, orthogonal Latin squares, permutations, Pierre Rosenstiehl
3 Comments
Easy to state, hard to solve?
I described here how Pablo Spiga and I showed that all but finitely many nontrivial switching classes of graphs with primitive automorphism group contain a graph with trivial automorphism group, and found the six exceptions. (The trivial switching classes are … Continue reading
Posted in exposition, open problems
Tagged graphs, homomorphisms, primitive groups, rigid graphs, switching classes, tournaments
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Solutions
The word “solutions” is much overused, even misused, now. When I see a van with “Cleaning solutions” on the side, I imagine it full of containers of ammonia or soapy water, while “Printing solutions” can only mean ink … But … Continue reading
Posted in books, teaching
Tagged Cambridge University Press, codes, Dan Hughes, designs, exercises, graphs, HigmanSims, Jack van Lint, MUBs, quaternary codes, Westfield College
1 Comment
Primitive graphs
A primitive graph is one whose automorphism group acts primitively on the vertices: that is, the group is transitive on the vertices, and there is no nontrivial equivalence relation which it preserves. This post is not about why primitive graphs … Continue reading
The arXiv
It will be absolutely clear to anyone who has given this blog more than a casual glance that I am a dinosaur mired in the 1960s or thereabouts, and quite out of tune with the modern world of Facebook, impact, … Continue reading
MathOverflow
Today I put a toe into the pool that is MathOverflow for the first time. My question was: Which graphs have the property that the number of ivertex induced subgraphs is at most i for some i<n/2 (where n is … Continue reading
Posted in doing mathematics, mathematics
Tagged graphs, MathOverflow, permutation groups, PlanetMO
8 Comments
Transitivity and synchronization
Let Sn be the symmetric group of all permutations of {1,…,n}, and Tn the full transformation monoid of all functions from this set to itself. Recently I have come to the metaconjecture that there is a fairly close analogy between … Continue reading
Posted in exposition, open problems
Tagged Dixon's theorem, endomorphisms, graphs, groups, semigroups, synchronization, synchronizing monoids
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Graph limits and random graphs
These ideas are quite new to me, and maybe my exposition of them is a bit incoherent; but I think there are some interesting questions here. An old problem of mine on random graphs with forbidden subgraphs may be illuminated … Continue reading
Posted in events, exposition, open problems
Tagged Endre Szemeredi, exchangeable measure, graphs, Laszlo Lovasz, limit
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