A counterexample to the Ringel circle problem: https://arxiv.org/abs/2112.05042, via https://gilkalai.wordpress.com/2021/12/11/to-cheer-you-up-in-difficult-times-34-ringel-circle-problem-solved-by-james-davies-chaya-keller-linda-kleist-shakhar-smorodinsky-and-bartosz-walczak/
Ringel asked whether systems of circles, tangent only in pairs, can be colored with O(1) colors so no two tangent circles have the same color. Five colors were known to be necessary but unknown to be sufficient; see the lead image of my old web page https://www.ics.uci.edu/~eppstein/junkyard/tangencies/
Now Davies, Keller, Kleist, Smorodinsky, and Walczak have found systems of circles requiring arbitrarily many colors.
TheoretiCS, a new diamond-open-access journal in all areas of theoretical computer science: https://theoretics.episciences.org/
It is being run as an overlay of arXiv, through the Episciences platform for such overlays, with Javier Esparza and Uri Zwick as editors-in-chief and a large and distinguished editorial board.
Just wrapping up my second week at the Banff International Research Station. This week's workshop is on Statistics and Machine Learning. The highlight, for an outsider like me, has definitely been Tselil Schramm's mini-course on the sum-of-squares algorithmic paradigm. A decade's worth of research nicely condensed into four one-hour lectures.
@eptf I knew about (and always use) -x, but -u is new to me, probably because I typically don't work much with environment variables. These days, though, python has mostly replaced bash scripts for me.
Five talks from CanaDAM 2021 introducing graph product structure theory and its applications:
This is probably the best / quickest introdoctrination to the topic currently available.
mh, death, suicide(?), local news
@bremner Nice article about him from when he first went missing:
Today I'm heading to the clinic to receive my first dose of the AstraZeneca vaccine. Ignoring the possibility that it might save me from death by covid, the worst case estimates suggest that this increases my odds of dying in the next 365 days from 1/444 to 1/442. I can live with that.
An implementation of the Product Structure Theorem for planar graphs, in Python:
Not exactly industrial-strength, and leans towards simplicity over performance. Still, it can decompose 100k-vertex triangulations in a few seconds. I'm open to feature requests.
@christianp Ha! I forgot that Canada and the UK share Remembrance Day.
11:00 was during my class today. It's surprisingly hard to stand still in front of a camera while waiting for a minute to elapse.
New blog post, Hex, books, and queues: https://11011110.github.io/blog/2020/11/10/hex-books-queues.html
And new arXiv preprint, Stack-number is not bounded by queue-number (with Vida Dujmović, Robert Hickingbotham, Pat Morin, and David R. Wood), https://arxiv.org/abs/2011.04195
How many integer colours are sufficient to colour an \(n\)-vertex planar graph so that the maximum colour encountered along any path of length at most 2 occurs only once along that path? It turns out that the correct answer is \(\Theta(\log n/\log\log\log n)\). The triple-log comes from the fact every planar graph is contained in the strong product of a planar 3-tree and a very simple graph.
if you like well-quantified risk info
Congratulations to my (now former) student, Luís Fernando Schulz Xavier da Silveira, who successfully defended his PhD thesis titled Turán Triangles, Cell Covers, Road Placement and Train Scheduling on Monday.
This is the first thesis defense I've taken part in where no two participants were in the same room.
Professor of Computer Science at Carleton University
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