four-color problem: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “four-color problem” mean?
A long-standing theorem in mathematics (now proven) that states any map on a plane can be colored using at most four colors such that no two adjacent regions share the same color.
Audio
Pronunciation
Definition
Meaning and Definition
A long-standing theorem in mathematics (now proven) that states any map on a plane can be colored using at most four colors such that no two adjacent regions share the same color.
A term also used metaphorically in computer science, logic, and problem-solving to refer to complex constraint satisfaction problems, particularly those involving partitioning or labeling under adjacency rules. The successful proof is a landmark in mathematical history and computational proof verification.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning. British English may occasionally use the spelling 'four-colour problem', though the hyphenated 'four-color' is standard in the fixed term.
Connotations
Identical in both varieties. Connotes high-level mathematical reasoning, historical significance, and computational complexity.
Frequency
Extremely low frequency in general discourse, used almost exclusively in mathematics, computer science, and related academic fields. Frequency is equal in both varieties within those domains.
Grammar
How to Use “four-color problem” in a Sentence
The four-color problem [VERB: was solved/proved/posed]to prove/solve/consider the four-color problemthe four-color problem for [OBJECT: planar graphs/maps]Vocabulary
Collocations
Examples
Examples of “four-color problem” in a Sentence
verb
British English
- Mathematicians sought to four-colour any planar map.
- The team attempted to four-colour the complex diagram.
American English
- The algorithm is designed to four-color the network graph efficiently.
- Early researchers failed to four-color all possible map configurations.
adjective
British English
- The four-colour theorem proof was controversial.
- It's a classic four-colour map problem.
American English
- The four-color map assumption is key.
- They studied four-color graph solutions.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core term in graph theory, topology, and history of mathematics. Used in lectures, papers, and textbooks.
Everyday
Extremely rare, only in educated discussion about mathematics or puzzles.
Technical
Precise term in mathematics and computer science, especially in algorithm design and formal proof theory.
Vocabulary
Synonyms of “four-color problem”
Strong
Neutral
Weak
Vocabulary
Antonyms of “four-color problem”
Watch out
Common Mistakes When Using “four-color problem”
- Calling it the 'four-colour problem' after its proof (should be 'theorem').
- Misspelling as 'for-color problem'.
- Using it to refer to any simple problem with four elements.
FAQ
Frequently Asked Questions
Yes, it is now a theorem. It was proven in 1976 by Kenneth Appel and Wolfgang Haken.
It was the first major theorem proven using substantial computer assistance, which raised philosophical questions about the nature of mathematical proof.
It applies equivalently to maps on a sphere. Maps on a torus (doughnut shape) can require up to seven colours.
Direct applications are limited, but the concepts underpin algorithms for frequency assignment in mobile networks, scheduling problems, and register allocation in compiler design.
A long-standing theorem in mathematics (now proven) that states any map on a plane can be colored using at most four colors such that no two adjacent regions share the same color.
Four-color problem is usually technical / academic in register.
Four-color problem: in British English it is pronounced /ˌfɔː ˈkʌlə ˌprɒbləm/, and in American English it is pronounced /ˌfɔr ˈkʌlər ˌprɑbləm/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “It's not a four-color problem (metaphorical: it's not that complex).”
Learning
Memory Aids
Mnemonic
Think of a world map: Can you color all countries so neighbours fight (same colour)? Only four crayons are needed for peace.
Conceptual Metaphor
A COMPLEX PUZZLE IS A MAP TO COLOR; LOGICAL CONSTRAINTS ARE PHYSICAL BORDERS.
Practice
Quiz
What does the four-color theorem guarantee?