ოთხი ფერის პრობლემა

ოთხ ფერით შეღებილი რუკის მაგალითი

ოთხი ფერის პრობლემა – ამ სახელწოდებით ცნობილია შემდეგი ამოცანა:

  • შესაძლებელია თუ არა სიბრტყეზე დახატული ნებისმიერი პოლიტიკური რუკა შეიღებოს მხოლოდ ოთხი ფერის გამოყენებით ისე, რომ არც ერთი მოსაზღვრე ქვეყანა არ აღმოჩნდეს ერთი და იმავე ფერით შეღებილი.

უფრო მათემატიკური სახით იგივე ამოცანა შეიძლება ჩამოვაყალიბოთ შემდეგნაირად:

  • შესაძლებელია თუ არა ნებისმიერი ბრტყელი გრაფის წვეროები შევღებოთ ოთხი ფერის გამოყენებით ისე, რომ ყოველი მომიჯნავე წვერო შეღებილი იყოს განსხვავებული ფერებით.

ოთხი ფერის ამოცანა პირველად დასვა ფ. გოსრიმ 1852 წელს. მასზე დადებითი პასუხი გასცეს ამერიკელმა მათემატიკოსებმა კ. აპელმა და ვ. ჰაკენმა 1976 წელს.

ოთხი ფერის პრობლემა პოპულარული მათემატიკური ლიტერატურის ერთ-ერთი საყვარელი თემაა. ყველაზე ხშირად მას სვამენ ზემოთ მოყვანილი სახით, პოლიტიკური რუკის შეღებვის შესახებ. თუმცა, რა თქმა უნდა, პრაქტიკული კარტოგრაფიის თვალსაზრისით ამოცანას დიდი მნიშვნელობა არ აქვს.

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