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GATE 2026 CH – Question 8

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________

a cube drawn as two squares joined by edges, with the corners a, b, c, d on the top face and e, f, g, h on the bottom face.
  1. 8
  2. 4
  3. 3
  4. 2

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Show answer and explanation

Correct answer: (D) 2

Explanation

A cube is a bipartite graph. Colour a corner with one colour, all its neighbours with the second colour, and then their neighbours with the first again. Every edge then joins different colours, since the cube has no odd cycles (the shortest cycle has 4 corners). One colour is not enough because every edge needs two colours, so the minimum is 2.