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.

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: 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.

For non-planar graphs, such solutions are computationally intractable," explained the researchers. The algorithm relies on the Kac-Ward formalism, a mathematical method that allows exact computation ...

Neo4j Inc. today announced a new serverless offering that dramatically simplifies the deployment of its graph database offering, making it easier to use with artificial intelligence applications. Most ...

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 ...

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