Question

Let (v) be a vertex of a connected graph (G). For (r ≥ 0) let (Gᵣ) be the subgraph of (G) induced by the vertices at a distance exactly (r) from (v). Prove that:
(χ(G) ≤ maxχ(Gᵣ) + χ(Gᵣ₊₁) : r ≥ 0).
a) True
b) False