How Does Graph Theory Shape Our World?
https://www.quantamagazine.org/how-does-graph-theory-shape-our-world-20250626
https://en.wikipedia.org/wiki/Graph_theory
Comments
* relational data/basis of knowledge graphs
* philosophy: Leibniz, 1714, monads, linking fundamental objects 😯
https://en.wikipedia.org/wiki/Monadology
#math #GraphTheory #Monadology #Leibniz #monads #KnowledgeGraphs #epistemology #philosophy
Them: "A new article is citing your research"
Me: "Ow, nice, which one? what's the research about?"
*checks paper*
The authors: we looked at the clustering coefficient [cite my paper]
Me: you don't say... THE clustering coefficient, uh! right, right...
Context: I wrote a paper discussing the differences between multiple different definitions of the clustering coefficient for weighted networks and how this can significantly affect the results; the paper citing my work does not even define which clustering coefficient they are using...
A friend showed me a leetcode problem yesterday at the Recurse Center:
Which led me to play for a bit on paper, then drafted a rough a visual toy:
https://codepen.io/fractalkitty/live/WbvJKgy
(I haven't actually done any leetcode problems because I often end up on paper and down rabbit holes)
Blog post: https://astrobeano.blogspot.com/2025/05/ergo-mech-keyboard-wiring-using-tutte-coxeter-graph.html
Building on T.G. Marbach's #GraphTheory idea to use the Heawood graph for a split keyboard #MechanicalKeyboard (see https://astrobeano.blogspot.com/2025/05/topology-meets-custom-keyboard-circuit.html), I've applied the larger Tutte-Coxeter (Tutte 8 Cage) to sketch diode-free 34, 36, 40, & 42 key #ErgonomicKeyboard PCB layouts.
I'm on a roll, two blog posts about #ErgonomicKeyboard design this week!
This one is about some cool #GraphTheory maths which has been used to design a #SplitMechanicalKeyboard and full #MechanicalKeyboard without diodes:
https://astrobeano.blogspot.com/2025/05/topology-meets-custom-keyboard-circuit.html
And earlier, about my custom #KeyboardLayout (which in hindsight might have fitted better on the hobby blog?):
https://blastedbio.blogspot.com/2025/05/what-have-you-done-to-your-keyboard.html
Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...
https://arxiv.org/abs/2505.13371
I am excited to see what developments follow on from here!
(Also that old adage: just as soon as you publish a survey (https://arxiv.org/abs/2501.03379) it is out of date.)
#math #mathematics #combinatorics #ExtremalCombinatorics #graphtheory #probability
We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the upper and lower bounds to a factor of $3+o(1)$. This improves the best known lower bound of $(1/4+o(1))k^2/\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. As a consequence, we disprove a conjecture of Fiz Pontiveros, Griffiths and Morris that the constant $1/4$ is sharp.
I am starting a new series on the blog for inquiries in math. I posted the first one today:
https://www.fractalkitty.com/inquiries-week-1-circle-shading/
This is the first of a series of guided inquiries in math. If a document is preferred over a blog post, the pdf file is below: Inquiries-Week 1_ Circle ShadingInquiries-Week 1_ Circle Shading.pdf622 KBdownload-circle Introduction When circles overlap they make lunes: or lenses: or other fun shapes: Activity Let's
A century-old enigma, graph theory and design
Behind a static form, there are connections, transformations and, above all, the elegance of mathematics.
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(Just finished writing my laudatio speech.)
Eoin Hurley will defend his PhD on Wednesday.
#combinatorics #graphtheory #ExtremalCombinatorics #probability #algorithms #math
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