Q4,paper 2,june12. The number of colors required to properly color the every vertices of planar graph.

Option(A) 2.                          (B)3     (c)4        (D)5.

Answer (D) 5.

Explanation. The number of colors needed to properly color any map is now the number of colors needed to color any planar graph. This problem was first posed in the nineteenth century, and it was quickly conjectured that in all cases four colors suffice. This was finally proved in 1976 with the aid of a computer. In 1879, Alfred Kempe gave a proof that was widely known, but was incorrect, though it was not until 1890 that this was noticed by Percy Heawood, who modified the proof to show that five colors suffice to color any planar graph.