ABSTRACT: We introduce the bichromatic triangle polynomial P G Δ ( k ) , a chromatic invariant that counts vertex colorings of a graph in which every designated triangular face uses exactly two colors ...

From powering search engines to securing data and optimizing networks, algorithms underpin nearly every aspect of modern technology. Understanding how efficiently they can solve problems — and where ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

Abstract: The graph coloring problem involves coloring the nodes of a graph using the minimum number of colors such that no two adjacent nodes share the same color. This NP-hard problem has various ...

Credit: Image generated by VentureBeat with FLUX-pro-1.1 Without data, enterprise AI isn't going to be successful. Getting all the data in one place and having the right type of data tools, including ...

Abstract: Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum ...

CEO Sam Altman called a strange graph in its GPT-5 presentation a ‘mega chart screwup.’ CEO Sam Altman called a strange graph in its GPT-5 presentation a ‘mega chart screwup.’ is a senior reporter ...

If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost.

The Detroit Tigers are having a great 2025 season as they sit on top of the American League. The team has the best record in the league (36-20) and is all set to make their second-straight postseason ...

Hey everyone! I recently passed the NVIDIA Data Science Professional Certification, and I'm thrilled to share some insights to help you on your journey. This is part of a series where I'll break down ...