The minimum number of colors needed to color a graph having n > 3 vert

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Module 3: Graph and Tree Algorithms

20222m

The minimum number of colors needed to color a graph having $n > 3$ vertices and 2 edges is
(i) 2
(ii) 3
(iii) 4
(iv) 1

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Answer: (i) 2

Graph with >3 vertices but only 2 edges is disconnected forest; at most needs 2 colors (bipartite, no odd cycle). Unless edge is loop, 2 colors suffice.

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