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Exercise 18 (Chapter Review)

Avg difficulty 2.5

Decide whether the following statements are true or false. Prove your answers.

  1. If two graph G1G_1 and G2G_2 have the same chromatic number, then they are isomorphic.

  2. If two graphs G1G_1 and G2G_2 have the same number of vertices and edges and have the same chromatic number, then they are isomorphic.

  3. If two graphs are isomorphic, then they have the same chromatic number.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §5.7 Chapter Summary, Chapter Review, Exercise 18

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Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.