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 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/
A century-old enigma, graph theory and design
Behind a static form, there are connections, transformations and, above all, the elegance of mathematics.
Discover MORE and SUBSCRIBE to our summary of news and updates through link: https://amusementlogic.com/general-news/a-century-old-enigma-graph-theory-and-design/
#graphtheory #mathematicaldesign #geometry #science #designscience #topology #computationaldesign #teoriadegrafos #diseñomatematico #geometria #ciencia #topologia #diseñocomputacional #sabiasque #saviezvousque #théoriedesgraphes
Revolutionizing Graph Theory: The Breakthrough in Edge Coloring Algorithms
In a remarkable leap forward, researchers have unveiled a groundbreaking algorithm for graph edge coloring that promises to drastically reduce computation time. This new approach, leveraging innovativ...
Ok, someone more familiar with graph theory tell me how to compute a minimum weight perfect matching on a complete graph with even-number of vertices? Or at least point me to a resource?
It's all either left as an exercise to the reader, extremely complex algorithms (Blossom or something?), or weird libraries, where apparently if I use it on complex graphs it's not necessary, but they then point me to even more complex papers.
Thought I had it solved but now it's returning a matching that's too small.
#graphtheory #computerscience #academia
Without formal training, the way I modeled physical distribution system #Infrastructure for utilities districts in my #Django app evolved significantly over time.
As I learned more about graph theory and simulation, I figured out how to model for both the physical structure and the logical aspects of their interconnection and behavior in various scenarios.
#GraphTheory #WaterInfrastructure #Modeling
1/6
This video is a really pretty visualization of the A* pathfinding algorithm using #OpenStreetMap road network data for #Chicago and #Rome as examples.
Calling all #igraph enthusiasts!
We've identified and fixed a bug in {ig.degree.betweenness} related to the cluster_edge_betweenness() function.
The issue stemmed from a grep() action used for subgraph identification.
A fix has been implemented, and an update has been pushed to CRAN—it will be available in the coming days.
In the meantime, you can reinstall from the main branch here: https://github.com/benyamindsmith/ig.degree.betweenness
A question for the (combinatorial) hive mind.
There are a lot of extremal results that are matched asymptotically by some probabilistic construction, but with some gap, often quite substantial. I'm thinking about the Ramsey numbers R(k,k) or R(3,k), but examples of this phenomenon are prevalent.
I'm curious, does someone out there know of good examples of (extremal) results where some probabilistic construction (e.g. via a random graph) is matched asymptotically, and very precisely?
Visualizing Interconnected Networks with Matplotlib and NetworkX
Learn to visualize complex networks using Network Visualization Matplotlib & NetworkX in Python. Create insightful visualizations & communicate complex data clearly! #NetworkVisualization #Python #Matplotlib #NetworkX #DataVisualization #GraphTheory
https://tech-champion.com/programming/python-programming/visualizing-interconnected-networks-with-matplotlib-and-networkx/
Efficiently Creating and Visualizing Symmetric Adjacency Matrices in Python
Master Python Adjacency Matrix techniques! Learn efficient creation, NetworkX visualization, & handling of large datasets. Represent & analyze complex relationships in your data. #PythonAdjacencyMatrix #GraphTheory #NetworkX #DataVisualization #DataScience #GraphAlgorithms
https://tech-champion.com/programming/python-programming/efficiently-creating-and-visualizing-symmetric-adjacency-matrices-in-python/
Network Graph Visualization: Improving Clarity in Dense Clusters with NetworkX
Improve Network Graph Visualization with NetworkX & Matplotlib! Learn simple yet effective strategies to enhance clarity, especially in dense clusters. Explore alternative layout algorithms & parameter adjustments for insightful data representation. #NetworkGraphVisualization #NetworkX #Matplotlib #DataVisualization #GraphTheory #Python
https://tech-champion.com/programming/python-programming/network-graph-visualization-improving-clarity-in-dense-clusters-with-networkx/
A post of @11011110 has reminded me that (after a year and a half lurking here) it's never too late for me to toot and pin an intro here.
I am a Canadian mathematician in the Netherlands, and I have been based at the University of Amsterdam since 2022. I also have some rich and longstanding ties to the UK, France, and Japan.
My interests are somewhere in the nexus of Combinatorics, Probability, and Algorithms. Specifically, I like graph colouring, random graphs, and probabilistic/extremal combinatorics. I have an appreciation for randomised algorithms, graph structure theory, and discrete geometry.
Around 2020, I began taking a more active role in the community, especially in efforts towards improved fairness and openness in science. I am proud to be part of a team that founded the journal, Innovations in Graph Theory (https://igt.centre-mersenne.org/), that launched in 2023. (That is probably the main reason I joined mathstodon!) I have also been a coordinator since 2020 of the informal research network, A Sparse (Graphs) Coalition (https://sparse-graphs.mimuw.edu.pl/), devoted to online collaborative workshops. In 2024, I helped spearhead the MathOA Diamond Open Access Stimulus Fund (https://www.mathoa.org/diamond-open-access-stimulus-fund/).
Until now, my posts have mostly been about scientific publishing and combinatorics.
#introduction
#openscience
#diamondopenaccess
#scientificpublishing
#openaccess
#RemoteConferences
#combinatorics
#graphtheory
#ExtremalCombinatorics
#probability
Revolutionizing Mathematics: The Rise of Automated Conjecturing with TxGraffiti
In a groundbreaking advancement for the field of mathematics, the newly introduced program TxGraffiti is set to automate the generation of mathematical conjectures, particularly within graph theory. T...
I'm doing some of my "follow the instructions for a change" #Sashiko, and came upon a bit that I think means I can't do everything that's left without a lot of stopping and starting.
Then I realised I have an actual graph theorist in the house who might see something I'd missed.
So I checked with @ColinTheMathmo, and he did spot something I'd missed, but it confirmed the impossibility.
I'll have to fudge it...
The "Bunkbed Conjecture" debunked:
#mathematics #graphtheory #physics #research #science
https://www.quantamagazine.org/maths-bunkbed-conjecture-has-been-debunked-20241101/
I asked the 6yo to colour a map with no adjacent countries getting the same colour. Of course its dual was K_4 so four colours were used.
I asked if he could use just three colours. He got colouring straight away. I decided to cushion the coming blow by saying "it might be hard"
"No, it's easy: just leave one of them blank"
