Computer Sciences > GATE 2026 SET-1 > Graph Algorithms
Let G(V, E) be a simple, undirected graph. A vertex cover of G is a subset V′ ⊆ V such that for every (u, v) ∈ E, u ∈ V′ or v ∈ V′. Let the size of the smallest vertex cover in G be k. Let S be any vertex cover of size k.

For a vertex v ∈ V, which of the following constraints will always ensure that v ∈ S?
A
The degree of v is at least k + 1
B
The vertex v is on a path of length k + 1
C
The vertex v is on a cycle of length k + 1
D
The vertex v is a part of a clique of size k

Correct : a

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