I took my second course in linear algebra with Robb, and it was one of the most entertaining courses of my first two years. My course notes – the only full set of notes I ever took in undergrad – were naturally interspersed with records of Robb's regular witty remarks and quotable quotes. When visiting my parents over the holidays, I dug out these notes, so I thought I'd share some of the memorable episodes from my time with him.

ROBB: Can I call this function \(\tilde{f}\)  "f twiddle" and this one \(\tilde{\tilde{f}}\)  "f twiddle twiddle"?
CLASS: Sure.
ROBB: So take \(\tilde{\tilde{f}}\ {}^*\) "f twiddle twiddle little star..."

(Introducing the notation ∃!)
ROBB: It means "there exists a unique..." but I always read it like it's a William Shatner thing. THERE EXISTS!

ROBB: You're defining this... it doesn't come from God. Especially since God doesn't exist.
CLASS: Ooooooooooooh
ROBB: Oooh, he has an opinion!

ROBB: An oval...
CLASS: Don't you mean an ellipse?
ROBB: Yeah, whatever the real term for that is.

ROBB: I'm going to avoid yellow chalk today, because I have a suspicion that one day they'll find that the stuff that makes it yellow is toxic. That's going to be someone's Ph.D. thesis one day, The Toxic Effects of Yellow Chalk, and I don't want to be part of the study group.

(After introducing the kernel as "the set of all stuff that gets killed by a map")
ROBB: The best bumper sticker I've ever seen had a picture of the colonel from KFC with "I am dead."

ROBB: If you're ever reading a paper, and they say they have to prove a technical lemma, brace yourself for some HORRIFIC MATH.

(Talking about stable/invariant sets)
ROBB: I use "invariant" instead of "stable." A stable set sounds like something for horses. I like horses, mind you, but they shouldn't be confused with mathematics.

You taught me, inspired me, and motivated me to continue on the path to becoming a mathematician. But more importantly, it was a lot of fun to know you. Thanks, Robb.

So if you've arrived at this website hoping for applications of graph theory in the great sport of cricket: I hate to disappoint you, but I don't have much. I thought about it long and hard, but I couldn't come up with anything that directly applies a pure graph theoretic result. Certainly there's a great deal of statistics involved in cricket, most famously the method derived by Duckworth and Lewis to set a target after a rain delay. There's quite a bit of geometry (and possibly some stochastic programming) in setting a field. There's a ton of interesting mathematics from a bunch of different fields behind Hawk-Eye; maybe they use graph theoretic algorithms under the hood? Your club league might benefit from some of the work done on various scheduling problems, and the international travel schedules could use some combinatorial optimization. Data science can apparently help you bowl out Tendulkar and applied math can help you decide when to declare. Graph theory can be a helpful tool for solving a number of these problems, but as for a pure graph theoretic situation that crops up in cricket? Can't think of any. Sorry.

(If you can think of a practical application of graph theory to the great sport of cricket, let me know in the comments!)

IWOCA 2011 group picture taken by the organizers

Two weeks after hosting CanaDAM, UVic was also the home of this year's International Workshop on Combinatorial Algorithms; there I presented a paper by myself, Jing Huang, and Xuding Zhu on cycle-transverse matchings. In the paper, we consider the C_k transverse matching problem: given a graph G, is there a matching M such that G-M contains no cycles of length k? We gave a polynomial-time algorithm for the case k=3, but showed that the problem is NP-complete when k ≥ 4. In fact, when k ≥ 4 is even, the problem is still NP-complete for bipartite graphs.

The case k = 4 has connections with the tatami tiling problem, as Frank Ruskey pointed out to us.

Click here to see the slides of the talk. (PDF)

University innings

Bowling

Fall of wickets: 1-22 (Rajinder, 1.3 ov), 2-32 (Peter, 2.6 ov), 3-40 (Kevin, retired, 4.4 ov), 4-56 (Raj, 7.3 ov), 5-64 (Prabhat, 8.6 ov), 6-66 (David, 9.3 ov), 7-98 (Ross, 13.3 ov), 8-98 (James, 13.5 ov), 9-104 (Shantanav, retired, 14.3 ov)

Highlights: Kevin opened our batting with a massive six into the adjacent pasture, bothering some sheep and losing the game ball. He eventually retired on 25* with an impressive strike rate of 227, thanks to a four and another long six. At the other end of the innings, Shantanav closed with three boundaries and a professional 26*. On a personal note, I hit my first-ever boundary on the way to scoring a season-high 8 runs.

Colts innings

Bowling

Fall of wickets: 1-11 (Ram, 2.1 ov), 2-11 (Trevor, 2.2 ov), 3-15 (Theo, 4.1 ov), 4-15 (Trenton, 4.4 ov), 5-25 (Brett, 5.6 ov), 6-29 (Riley, 6.5 ov), 7-31 (YJ, 7.2 ov), 8-31 (Vatsal, 7.4 ov)

Highlights: After our innings, the clouds closed in further; with raindrops suspended in the air, we had to finish the Colts quickly to fend off a draw. Our confident bowlers did the job in less than 8 overs: David taking four wickets, Kevin one, and Raj three. Brett, a new University recruit playing this match for the Colts, put his baseball experience to work with a boundary in his debut innings to score a total of six.

RESULT: University 104-(7+2) beat Colts 31-8 by 73 runs.

CanaDAM group photo taken by the conference organizers

This year, I had the pleasure of attending (and helping organize) CanaDAM, which was held at UVic. I gave a talk in the Structured Graphs and Algorithms session, titled "Partitioning graphs via edge-coloured homomorphisms". In it, I announced some recently-submitted results on the monopolar partition problem and related problems. The main result unifies all currently known polynomial-time monopolarity results: it reduces the problem to 2SAT for a very large graph class, which contains

• claw-free graphs
• chordal graphs
• co-comparability graphs
• all graphs with no induced cycle of length ≥ 5

A similar technique can be used to solve the unipolar partition problem – which asks whether a (general) graph can be partitioned into a clique and a disjoint union of cliques – in polynomial time.

Click here to see the slides of this talk.

University innings

Bowling

Fall of wickets: 1-6 (Shelby, 0.5 ov), 2-48 (Yaju, 4.6 ov), 3-55 (Rajinder, retired, 5.3 ov), 4-62 (Shantanav, 6.5 ov), 5-112 (Doug, retired, 11.1 ov), 6-112 (Miles, 11.4 ov), 7-119 (Zain, retired, 12.3 ov)

Highlights: We had plenty of boundaries this match from the fast field and slower bowling. Rajinder, Doug, and Zain all retired after making their quarter-centuries. Kim struck back with some first-class bowling — taking one wicket while conceding only a four in her first two overs — but we were still able to set a good target of 140.

Wicket Maidens innings

Bowling

Fall of wickets: 1-13 (Laura, 4.2 ov), 2-17 (Shveta, 5.4 ov), 3-33 (Kim, 9.5 ov), 4-49 (Jenny, 15.4 ov)

Highlights: With some highly economical bowling from Prabhat, Rajinder, and Shelby, we managed to hold the Wicket Maidens to 51 runs, twenty short of their target.

RESULT: University 140-(4+3) beat Wicket Maidens 102-4 by 38 runs.

Metchosin innings

Bowling

Fall of wickets: 1-41 (Ty, 4.3 ov), 2-58 (Jordan, 7.6 ov), 3-75 (Jade, 9.6 ov), 4-87 (Saul, 12.4 ov), 5-96 (Rick, retired, 13.4 ov), 6-108 (Blair, 14.4 ov)

University innings

Bowling

Fall of wickets: 1-10 (Yaju, 2.2 ov), 2-23 (Manni, 4.6 ov), 3-23 (Kevin, 5.2 ov), 4-23 (Peter, 5.3 ov), 5-62 (Shantanav, retired, 9.5 ov), 6-65 (Prabhat, 10.4 ov), 7-71 (Ram, 12.5 ov), 8-73 (Miles, 13.1 ov)

RESULT: Metchosin 113-(5+1) beat University 88-(7+1) by 25 runs.

With another election coming up, I thought it would be a good idea to revisit this post about public spending. The political media is naturally concerned with changes — a few billion dollars in new programs here or spending cuts there — but it's hard to understand changes without having some sort of baseline. This chart (which I made from the Treasury Board's 2011 estimates) should give some context to the coming weeks' campaign.

Edit: In addition to the spending on this chart, the federal government spends $30.3 billion on federal debt charges. Forgot to put that in, and it's too late to add it now... It'll have to wait to the next revisit!

Beagle innings

Bowling

Fall of wickets: 1-4 (Andy, 0.5 ov), 2-4 (Steve, 0.6 ov), 3-12 (Big Andy, 1.4 ov), 4-15 (Prabh, 2.1 ov), 5-40 (Keith, 7.5 ov), 6-60 (Kevin, retired, 9.2 ov), 7-91 (Ian, 11.5 ov), 8-95 (Scott, 13.1 ov), 9-98 (James, 13.6 ov)

Highlights: We got some amazing bowling from Doug, who took a hat trick separated over his first two overs. I thought we were doing great after taking four wickets for 15 runs in two overs, but was soon silenced by a dominant batting performance from Kevin (30 runs off 20 balls, including 3 sixes). It was a strange day for wides — we conceded 23 — but it must have been the rainy sunset, as the Beagle's bowlers had similar figures.

University innings

Bowling

Fall of wickets: 1-18 (Kevin, 2.4 ov), 2-39 (Prince, retired, 5.3 ov), 3-49 (Miles, 7.4 ov), 4-51 (Doug, 7.5 ov), 5-61 (Mike, 8.6 ov), 6-91 (Shantanav, 13.1 ov)

Highlights: Prince kept the wicketkeeping pads on and opened our batting with a strong 25. Miles scored a respectable 2 runs in his cricket-playing debut. The sixth-wicket partnership of Ram and Shantanav scored 30 runs to set up a dramatic finish. With eight runs needed from six balls, Shantanav was run out looking for a second run. After facing the last of the wides, Ram hit a single to put Yaju on strike for the last ball. Unfortunately, the defensive field allowed only a single and our innings ended three runs short of victory.

RESULT: Beagle 98-(8+1) beat University 95-(5+1) by three runs.

In the hopes of freeing up some brainpower for the work I'm supposed to be doing right now, I've turned to the collective wisdom of MathOverflow. If you know of any work that has been done on this problem, I'd be much obliged if you added an answer to my question there.