Blog in Combinatorics and Probability
Welcome to my blog on Combinatorics and Probability!
Here, I’ll share recent preprints by various authors in these fields, highlighting topics that capture my interest. You’ll also find posts about noteworthy academic events, as well as intriguing problems in probability and combinatorics. Whether you’re a fellow researcher, a student, or simply curious about the beauty of mathematics, I hope you’ll discover something interesting here.
Preprints in July 2025
In Combinatorics by July 12
- Spectra of high-dimensional sparse random geometric graphs, Yifan Cao and Yizhe Zhu,
https://arxiv.org/abs/2507.06556 - Bounded diameter monochromatic component covers, Alexey Pokrovskiy. https://arxiv.org/abs/2507.05842
- Hamiltonicity and structure of connected biclaw-free graphs, Alexey Pokrovskiy, Xiaoan Yang. https://arxiv.org/abs/2507.05836
- When does a tree activate the random graph?, Asaf Cohen Antonir, Yuval Peled, Asaf Shapira, Mykhaylo Tyomkyn, Maksim Zhukovskii. https://arxiv.org/abs/2507.05697
- Off-Diagonal Ramsey Numbers for Linear Hypergraphs, Xiaoyu He, Jiaxi Nie, Yuval Wigderson, Hung-Hsun Hans Yu. https://arxiv.org/abs/2507.05641
- The Saturation Number for the Diamond is Linear, Maria-Romina Ivan, Sean Jaffe. https://arxiv.org/abs/2507.05122
- Hypergraph Turán problem of the generalized triangle with bounded matching number Jian Wang, Wenbin Wang, Weihua Yang. https://arxiv.org/abs/2507.04579
- The Hamilton cycle space of random regular graphs and randomly perturbed graphsDan Hefetz, Michael Krivelevich. https://arxiv.org/abs/2507.04488
- Minimum degree and sparse connected spanning subgraphsTing Huang, Yanbo Zhang, Yaojun Chen. https://arxiv.org/abs/2507.03264
- The independence and clique cover numbers of the squarefree graph Boris Alexeev, Dustin G. Mixon, Will Sawin. https://arxiv.org/abs/2507.01928
In Probability
- The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spacesS. V. Dzhenzher, V. Zh. Sakbaev. https://arxiv.org/abs/2507.07658
Interesting articles
Courses from professors around the globe
- Extremal Combinatorics by Jonathan Noel at the University of Victoria. [link]
- Extremal Graph theory by Math Geeks. [link]