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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 wellknown in the algebraic graph theory community for a number of remarkable achievements, including … Continue reading
Posted in events
Tagged Alan Hoffman, algebraic graph theory, eigenvalues, Laszlo Lovasz, optimization, WIllem Haemers
1 Comment
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
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
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
Tagged doubly transitive groups, eigenvalues, Ramsey's theorem
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