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Tag Archives: graphs
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 non-trivial 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 i-vertex 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
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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 meta-conjecture 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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Bases
Sometimes you have to make things more complicated in order to make them simpler. My old friend Aiden Bruen visited this week, and told me about a paper by him and his son Trevor which has just appeared in the … Continue reading
Posted in exposition, mathematics, open problems
Tagged graphs, matroids, vector spaces
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