Lose the beamer navigation symbols!!

We’re all getting ready here for next week’s Australian Math Society conference in Adelaide, so I’ve been watching a few practice talks. Watching these, along with a few other recent talks,  reminded me of a pet peeve.

Nowadays, even in mathematics conferences, most talks are computer presentations, and most of these are prepared using Till Tantau’s beamer package for LaTeX.

Although beamer is amazingly good – or perhaps because beamer is amazingly good – its sheer ubiquity means that so many talks “look the same”.

And one way in which they look the same is that although I have never seen anyone use them in a talk, almost everyone seems to keep the default navigation symbols at the bottom corner of every page, where they often overlap the content and generally clutter the page.

But it is so easy to turn them off – just add

\setbeamertemplate{navigation symbols}{}

before the beginning of the document and away they go!

Graphs with integer flow roots

I’ve just uploaded a new version of a paper on graphs with integer flow roots to the arxiv. This is a joint paper with the matroid theorist Joe Kung from University of North Texas.

It is basically a dual version of the old problem of characterising graphs whose chromatic polynomials have integer roots. Chordal graphs, which are built up from a single vertex by repeatedly adding a new vertex adjacent to a clique, are one such class of graphs. But there are lots of non-chordal examples, and it seems hopeless to try and classify them all.

We considered the dual problem of the graphs whose flow polynomials have integer roots. Again there is an obvious class of examples, namely the planar duals of chordal graphs, but in this case there are no other examples. So the punchline of our paper is that “the obvious examples are the only examples”.

In matroid terms, the result says that a cographic matroid with integer characteristic roots is necessarily supersolvable.

We needed the new version because a student at MIT, Maria Monks, spotted a (fixable) error in the first version. This was despite the paper having been refereed and accepted already! So the power of the arxiv has saved Joe and I some red faces.