Tag Archives: eigenvalues

Hoffman, Lovász and Haemers

At the weekend I attended remotely a memorial session for Alan Hoffman, organised by Bill Pulleyblank. I found it informative, as well as moving. Hoffman is well-known in the algebraic graph theory community for a number of remarkable achievements, including … Continue reading

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More on derangements

Francis Bacon, in The New Organon, developed a famous metaphor: Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant, they only collect and use; the reasoners … Continue reading

Perth, week 4

And now the time in Adelaide and Perth is over. We are back in London, having arrived on the same day as we left Australia. This was the first time I have done this, and I really don’t recommend it. … Continue reading

Posted in exposition, synchronization | | 2 Comments

Solution to the Clebsch puzzle

Here is the solution to the puzzle about the Clebsch graph I posed at the weekend. Since Gordon and Tony (and probably others) have already solved it, I am giving you my solution now. The puzzle was: Suppose we delete … Continue reading

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Partitions into Petersens

There is a lovely algebraic argument to prove that the complete graph on ten vertices (which has 45 edges) cannot be partitioned into three copies of the Petersen graph (which has 15 edges). Sebastian Cioaba asked me: for which m … Continue reading

Posted in exposition, open problems | | 10 Comments

Fibonacci numbers, 3

The Fibonacci recurrence, an = an−1+an−2 is linear. This might suggest either of two things to you, depending on your background: Like a linear differential equation, its solutions obey the superposition principle; the sum of solutions is a solution, and a multiple … Continue reading

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