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graph theory

Latest Articles

A video depiction of shifting boundaries in Colorado illustrates the endless possibilities for drawing Congressional districts.
applied math

How Math Has Changed the Shape of Gerrymandering

By Mike Orcutt
June 1, 2023
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New tools make it possible to detect hidden manipulation of maps.

A visual argument explaining why the Ramsey number of three is six.
graph theory

A Very Big Small Leap Forward in Graph Theory

By Leila Sloman
May 2, 2023
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Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

combinatorics

The Number 15 Describes the Secret Limit of an Infinite Grid

By Kevin Hartnett
April 20, 2023
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The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

algorithms

How Randomness Improves Algorithms

By Ben Brubaker
April 3, 2023
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Unpredictability can help computer scientists solve otherwise intractable problems.

Quantized Columns

The Colorful Problem That Has Long Frustrated Mathematicians

By David S. Richeson
March 29, 2023
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The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

a small human figure stands on a golden geometric structure while the sky is full of curving pink and purple grids
graph theory

Quantum Field Theory Pries Open Mathematical Puzzle

By Leila Sloman
February 16, 2023
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Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

Shang-Hua Teng in a blazer on a street
Q&A

The Computer Scientist Who Finds Life Lessons in Games

By Ben Brubaker
January 25, 2023
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In Shang-Hua Teng’s work, theoretical and practical questions have long been intertwined. Now he’s turning his focus to the impractical.

graph theory

Finally, a Fast Algorithm for Shortest Paths on Negative Graphs

By Ben Brubaker
January 18, 2023
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Researchers can now find the shortest route through a network nearly as fast as theoretically possible, even when some steps can cancel out others.

cryptography

How Do You Prove a Secret?

By Sheon Han
October 11, 2022
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Zero-knowledge proofs allow researchers to prove their knowledge without divulging the knowledge itself.


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