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 ...

Graph cover problems form a critical area within discrete optimisation and theoretical computer science, addressing the challenge of selecting subsets of vertices (or edges) that satisfy predetermined ...

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 ...

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.

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...

Prefer Newsweek on Google to see more of our trusted coverage when you search. Young adults are graduating from college and heading out into the world, but a growing number of hiring managers are ...