Abstract: In this paper, a four-color coloring algorithm for maximal planar graphs with finite boundary is proposed, which aims to explore the four-color coloring method for complex planar graphs.

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

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: In this paper, Heawood's counterexample graph is artificially colored by using the algorithm of planar graph four-colorable based on path homotopy search, which verifies the feasibility and ...

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.

Google’s June 2025 Core Update just finished. What’s notable is that while some say it was a big update, it didn’t feel disruptive, indicating that the changes may have been more subtle than game ...

Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as ...

Graph theory is an integral component of algorithm design that underlies sparse matrices, relational databases, and networks. Improving the performance of graph algorithms has direct implications to ...

Java program demonstrating Mario, Zelda, and Pokemon to be NP-hard. Also includes algorithms for planarity testing, planar embedding, and graph drawing.