Four-Color Problem definition of Four-Color Problem in the Free Online Encyclopedia.

four-color problem [¦fȯr ′kəl·ər ‚präb·ləm]

(mathematics)

The problem of proving the statement that, given any map in the plane, it is possible to color the regions with four colors so that any two regions with a common boundary have different colors.

Four-Color Problem

the problem of whether four different colors are sufficient to color any map so that no two regions having a common boundary segment have the same color. Although the conjecture that four colors are enough was proved for all known special cases, the problem long remained unsolved. Not until 1976 was a report of a rigorous mathematical proof published.

First formulated as a mathematical problem in the mid-19th century, the four-color problem became widely known through the lectures of the British mathematician A. de Morgan. A rigorous formulation of the problem requires that the regions in question be bounded by Jordan curves—that is, by simple closed curves. It can be easily proved that five colors are always sufficient to color such a map.

In the corresponding problem for space, no number of colors is sufficient.

REFERENCE

Appel, K., and W. Haken. Bulletin of the American Mathematical Society, vol. 82, no. 5, pp. 711–12.

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No references found	The four-color problem poses this hypothesis: Every map can be colored with at most four colors in such a way that all neighboring countries are colored differently. Four Colors Suffice: How the Map Problem Was Solved by Science News	Four Arts Four Books four colour map theorem four colour theorem Four Families of China Four Forest Cantons, the Four Freedoms Four Horsemen Four Horsemen of the Apocalypse Four Horsemen of the Apocalypse, The Four Hundred Four Hundred, Council of the Four Lakes four laws of black hole mechanics Four Mile Creek State Park Four Noble Truths Four Thirds system four-address four-ball tester Four-Bar Linkage four-by-four four-centered arch four-centered pointed arch four-channel sound system four-color printing Four-Color Problem four-color process four-color separation process four-colour glossies four-colour map problem four-course radio range station four-crib barn four-current density Four-Cycle Engine four-degree calorie four-factor formula four-force four-frequency diplex telegraphy four-group Four-H clubs Four-Horned Antelope four-hundred-day clock four-in-hand four-layer device four-layer diode four-layer transistor four-leaf four-leaved flower four-level laser four-limbed core four-o'clock	Four Year College Four year degree Four Year Strong Four Young Sneaker Heads four-address Four-Arm Radial Open Maze Four-Arm Spiral Antenna four-bagger Four-ball four-ball tester Four-bar linkage four-by-four four-by-four four-by-fours four-by-fours four-by-two Four-C four-card monte Four-Cascaded Single-Stage Distributed Amplifier four-centered arch four-centered arch four-centered pointed arch four-centered pointed arch four-chamber method four-channel sound system four-color Four-color pen Four-color printing Four-Color Problem Four-color process Four-color process Four-color process four-color separation process four-colour four-colour glossies Four-Colour Map Problem Four-colour printing Four-cornered Four-Couple Module four-course radio range station four-crib barn Four-current four-current density four-cycle Four-Cycle Engine Four-cylinder Four-day weekend four-deal bridge four-degree calorie Four-Digit Year four-dimensional four-dimensional four-dimensional four-dimensional four-dimensional Four-Dimensional Data Assimilation Four-dimensional painting Four-dimensional space Four-dimensional space

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The four-color problem poses this hypothesis: Every map can be colored with at most four colors in such a way that all neighboring countries are colored differently.

Four Colors Suffice: How the Map Problem Was Solved by Science News

Four Arts

Four Books

four colour map theorem

four colour theorem

Four Families of China

Four Forest Cantons, the

Four Freedoms

Four Horsemen

Four Horsemen of the Apocalypse

Four Horsemen of the Apocalypse, The

Four Hundred