Sometimes, no matter how much everyone wants to get along, the way your friend group is set up makes it mathematically impossible to agree on anything.
March 20, 2026
Original Paper
Counting Strict Gridlock on Graphs
arXiv · 2603.18289
The Takeaway
Researchers discovered that certain network layouts create 'strict gridlock' states that act as geometric roadblocks to consensus. By counting these states, they can now measure exactly how much a specific group's connections will hinder them from ever agreeing on a common goal.
From the abstract
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to study how coloring problems can be solved by groups of individuals on a graph, which has led to new insights into network structure, group dynamics, and individual human behavior. Despite this newfound utility, the exact nature of these distributed coloring probl