Let N>2$N>2$ be a positive integer and G$G$ be a simple graph satisfies: (1)the maximal degree of G is N; (2)the clique number of G is N. I
- the maximal degree of $G$ is $N$
- the clique number of $G$ is $N$.
I want to ask if there exists a vertex independent set I$I$ in V(G)$V(G)$ such that for every N $N$-order complete subgraph H$H$ of G$G$,the the intersection of I$I$ and V(H)$V(H)$ is not empty,if. If not,please please give a counterexample.