Computational Combinatorics

Month: February, 2013

Computational Combinatorics Roundup: February 2013

In this month’s roundup, we have an article about computation in mathematics, and four research papers on wildly different problems.
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New Page: Syllabus

I’ve added a new page to the top bar of the blog: a syllabus! Part of the goal of this blog is to develop a set of lecture materials for a future topics course in Computational Combinatorics. Since we are a few topics in, I thought it would be good to organize them by topic in a somewhat reasonable order (and the order I would present them in a course). As part of that effort, I have also placed a few topics on the list for future posts. Take a look!

Generating Fullerenes

Today, we discuss “Generation of Fullerenes” by Brinkmann, Goedgebuer, and McKay, recently published in the Journal of Chemical Information and Modeling. A fullerene for our purposes is a cubic planar graph where every face has length 5 or 6. However, the definition of fullerene as a molecule is valuable as well (and why this paper was published in a chemistry journal). Since we previously discussed generating cubic graphs, we could use that algorithm and restrict our output to graphs that satisfy our requirements, but this method is wasteful as there are many more cubic graphs of order n than fullerenes of order n. Since their method uses canonical deletion, we only need to describe our base objects and our augmentation step.
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Computational Combinatorics Roundup: December-January

I’m a little late in compiling the late December to January roundup, but here we go. As always, send me an email if you have a blog post, paper, or other resource that I can put in the next roundup.
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