Graph Theory @graph_theory
One #proposition, #definition, #conjecture, #theorem a day. Berkeley, CA Joined June 2013-
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Some Tribonacci Conjectures Jeffrey Shalitt arxiv.org/abs/2210.03996
Local and global expansion in random geometric graphs. arXiv:2210.00158 arxiv.org/abs/2210.00158
How to cut a discrete cake fairly arxiv.org/abs/2209.01348
George Shevchenko: My heart breaks — Yuliya Zdanowska, my former (although everything is former for her now) student, colleague from summer schools, rock climbing friend, was killed that night. She was only 21 years old.
This is Yulia Zdanovska. She was 21. One of Europe’s best young mathematicians, a winner of European Math Olympics in 2017. She died under RU shelling in Kharkiv. R.I.P. Yulia. #StandWithUkraine
Rainbow Perfect and Near-Perfect Matchings in Complete Graphs with Edges Colored by Circular Distance. (arXiv:2012.06083v1 [math.CO]) dlvr.it/RnZsxM
Occupancy fraction, fractional colouring, and triangle fraction. (arXiv:1812.11152v2 [math.CO] UPDATED) dlvr.it/RnbYbd
New modular squaring depth lower bounds by Ryan Williams and Benjamin Wesolowski (@rrwilliams @BenjWeso). Such lower bounds strengthen our confidence in the sequentiality of RSA- and Sloth-based VDFs. Check out the cash bounties in section 7.1 💸 eprint.iacr.org/2020/1461.pdf
Here’s one in which each vertex has either four or eleven neighbours. (You can see two stars formed by the two vertices that have 11 neighbours; the others have 4.)
This is the Harborth graph, the simplest known planar graph in which all the edges are the same length and every vertex has exactly four neighbours.
Efficient Computation of High-Order Line Graphs of Hypergraphs. (arXiv:2010.11448v1 [cs.DM]) dlvr.it/Rk9CWK
List of problems posed by Paul Erdős. This includes still open problems, along with the associated prize, if applicable. Maintained by Fan Chung math.ucsd.edu/~erdosproblems…
A while ago, I tweeted that I hoped Cambridge would allow us to post our online lectures publicly. I'm delighted to say that they do indeed allow this, so I shall be posting my course Topics in Combinatorics on YouTube as I give it. 1/
This is the ideal topological ring. You may not like it but this is what peak performance looks like.
"Things a Graph Theorist Should Do at Least Once" …putationalcombinatorics.wordpress.com/2012/09/28/thi…
The Shrikhande graph (L) and the Rook's graph (R) are the smallest pair of non-isomorphic, strongly regular graphs with the same parameters* that are 2 WL equivalent i.e. can't be distinguished by the 2 Weisfeiler-Leman graph isomorphism test.
🗣️ Our preprint with Henry Towsner @htowsner is out! "Hypergraph regularity and higher arity VC-dimension" arxiv.org/abs/2010.00726 Phew this one took a minute. More details coming soon!
Hamza Alsamraee came to the U.S. as a refugee in 2014. Today is publication day for his charming, conversational, stimulating book on mathematical paradoxes. Did I mention that he's 18, and this is his *second* book? amazon.com//dp/B08HVMC3YZ/
Old but gold: Cursed tree with a cycle.
You probably think the McGee graph stays still on the pages of your textbooks, but whenever you’re not looking at it, this is what it does.
Tınaz Ekim @tinazekim
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