CMS Winter Meeting 2010
I appreciate everyone who looked at my slides instead of out the window during my talk.
My talk at the Canadian Mathematics Society's 2010 Winter Meeting was my first-ever conference presentation. The talk was scheduled at 4:30 in a hotel suite halfway up the building, so we were treated to the beautifully distracting sunset in the phone picture above.
I spoke about the structural characterization (by "well-formed sequences") of claw-free monopolar graphs and the resulting polynomial-time recognition algorithm. It was based on the research I did in my last year of undergrad and was submitted as "The polarity and monopolarity of claw-free graphs."
ROSS CHURCHLEY, University of Victoria
Monopolar claw-free graphsA graph is called monopolar if its vertices can be partitioned into an independent set and a disjoint union of cliques. Monopolar graphs, which include all bipartite and split graphs, form an important subclass of the so-called polar graphs. We present a structural characterization of monopolar claw-free graphs which suggests a simple \(O(n^3)\) algorithm for their recognition. This contrasts with the NP-completeness of related recognition problems, including those for monopolar graphs in general and for polar claw-free graphs.
Discrete Math Seminars 2010
UVic's math department, like many universities, holds a regular discrete math seminar. I gave a series of three talks in the Fall 2010 semester: two on monopolar claw-free graphs (which I condensed into my CMS Winter Meeting talk), and one based on Adrian Bondy's excellent paper Short Proofs of Classical Theorems.
In the last talk, Graph theory haiku: three short and beautiful proofs, I covered the first three proofs of that paper: of Ore's theorem, Brooks' theorem, and Vizing's theorem. For a little bit of fun, I rewrote Bondy's proofs in haiku form (although I had to resort to tanka for the second):
Ore's Theorem
A red-blue \(K_n\):
bluest Hamilton circuit
lies fully in \(G\).
Brooks' Theorem
Greedily colour,
ensuring neighbours follow
all except the last.Choose the last vertex wisely:
friend of few or of leaders.
Vizing's Theorem
Induction on \(n\).
Swap available colours
and find SDR.
Click here to see the slides of the talk. (PDF) Their design was made possible by the answers to a TeX StackExchange question I posed while making the slides.
The Edmonton Eulers
I was quite surprised the other day when I read this Division by Zero post:
A few years ago I found an alteration of the logo of the Edmonton Oilers (a Canadian hockey team in the NHL) in which “Oilers” was replaced with “Eulers.” I printed it and hung it outside my office door. Now I can’t find the original, but you can see a scanned copy on the left.
As it happens, I did a webcomic a few years ago called "Isotopes of Bismuth" and actually used this joke for the comic on October 2, 2007. Interestingly, it's not the same image (my version had serifs on the "U"), so Dave Richeson's original source must have been someone else with the same idea at the same time. Unfortunately, I too had lost my original editable file, but it wasn't hard to reconstruct one:
