There are (at least) two (apparently) unrelated classes of graphs called "parity graphs". One is the class of graphs in which the size of a maximal independent set is fixed mod 2. The other is the class in which the length of an induced u-v-path is fixed mod 2 for all pairs of vertices u,v. By coincidence, both are somewhat connected to research projects of mine, but the overloaded terminology is annoying.

The slope number of a graph G is the minimum number of distinct gradients of the edges in a straight line drawing of G.

An open problem that is very nice in my opinion: When Δ(G)≤3 the slope number of G is at most 4. For any k there is a graph G with Δ(G)=5 and slope number >k. But what about Δ(G)=4?

Not really my area at all but I like questions like this: where's the boundary?

When I add say 579 and 345, my inner monologue says "eight *nine* one *two* four nine hundred and twenty four!"

University of Strathclyde proposes to axe combinatorics and their three strong combinatorics faculty members: https://cameroncounts.wordpress.com/2019/06/19/combinatorics-at-strathclyde/

via https://gowers.wordpress.com/2019/06/19/the-fate-of-combinatorics-at-strathclyde/

This comes despite the group being both strong in research and important in undergraduate education. The apparent cause is Strathclyde's placement of combinatorics in computer science rather than in mathematics and in their use of standards aimed more at computer science than mathematics (like bringing in large grants).

The other day I was thinking about graphs that have degree sequence 1,3,3,3,... such graphs can't be bipartite, so I was wondering whether it is possible for such a graph to have no even cycle. It turns out that graphs with no even cycle have at most (3n-3)/2 edges (I think), whereas my graphs have exactly (3n-2)/2 edges!

No maths for Europe: https://plus.maths.org/content/democratic-dilemmas

Sadly, the EU parliament has passed up a chance to find a nice (or even not-so-nice) formula for its apportionment of seats to countries (see https://en.wikipedia.org/wiki/Highest_averages_method for several possible principled methods for doing this), instead opting for back-room deals and numbers pulled out of a hat.

Is oeis for graph sequences feasible? Would canonical labellings and graph6 be enough or have I overlooked something (I don't understand these things). Toy use case: I come across the graphs obtained from even cycles by adding edges between opposite vertices. I write a program that generates the first ten graph6 reps and search them. The oegs entry tells me (amongst other things) hey those are also the mobius ladders!

1. Advertising shits in your head, it is a form of visual and psychological pollution.

2. Removing/Replacing/Defacing advertising is not vandalism, it is an act of tidying up that is both legally and morally defensible.

3. The Visual Realm is a Public Realm, it is part of the commons, it belongs to everyone, so nobody should be able to own it.

4. Outdoor Advertising can and should be banned, Sao Paulo did it in 2006, Grenoble followed suit in 2015.

Came across the fibonacci word the other day: s₀=0 s₁=01 sᵢ =sᵢ₋₁||sᵢ₋₂ (string concatenation). The limit is 0100101001001... seems to have only a passing resemblance to the fib numbers... but look at y=x/φ in R² and consider where it intersects the grid with vertices in N² - write a 0 when it intersects a vertical line and 1 when it intersects a horizontal line and you get 0100101001001... !!

https://en.wikipedia.org/wiki/Fibonacci_word

For some silly reason I have been in base 4 this afternoon. At first I was converting back and forth from base 10, but (surprisingly) quickly I got used to doing arithmetic directly without translation. Unfortunately I can't seem to do the same thing with currencies; I've been in the Czech republic for six months and I still think in Euros (apart from beer)

From the amazon review of one of the volumes of Gibbons "History of the Decline and Fall of the Roman Empire":

"The Romans developed an extreme toughness and vindictiveness on account of being made fun of by uncouth barbarians for the sissy "W" sound of the V in classical Latin. Every time a strapping, macho gaul heard the pathetic-sounding 'weeny weedy weesy' and broke into a raucous, howling laughter, every Roman in earshot burned with shame and dreams of revenge."

Mathematician, computer scientist, bassist, knitter?

Joined Jan 2018