Tag Archives: graphs

Graphs on groups, 3

Posted on 07/02/2021 by Peter Cameron

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 →

Posted in Uncategorized | Tagged , , , , | 2 Comments

G2D2, 1: setting the scene

Posted on 12/08/2019 by Peter Cameron

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 , , , , , , , , | 1 Comment

OuLiPo

Posted on 08/01/2015 by Peter Cameron

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 , , , , , , , , , | 3 Comments

Easy to state, hard to solve?

Posted on 31/07/2014 by Peter Cameron

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 , , , , , | Leave a comment

Solutions

Posted on 08/10/2013 by Peter Cameron

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 , , , , , , , , , , | 1 Comment

Primitive graphs

Posted on 11/01/2013 by Peter Cameron

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 →

Posted in open problems | Tagged , , | Leave a comment

The arXiv

Posted on 19/08/2011 by Peter Cameron

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 →

Posted in exposition, open problems, the Web | Tagged , , | 4 Comments

MathOverflow

Posted on 05/08/2011 by Peter Cameron

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 , , , | 8 Comments

Transitivity and synchronization

Posted on 15/07/2011 by Peter Cameron

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 , , , , , , | Leave a comment

Graph limits and random graphs

Posted on 19/05/2011 by Peter Cameron

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 , , , , | Leave a comment