Existence of a graph with independence number three and eviction number five

Determine whether there exists a graph G with independence number α(G)=3 and eviction number e^∞(G)=5.

Background

The paper recalls that graphs with independence number 3 have eviction number at most 5, but does not establish whether the upper bound is attained. Thus, the unresolved issue is whether the value 5 is realizable by any graph with α(G)=3.

References

It is unknown whether there exists a graph $G$ such that $\alpha(G)=3$ and $e{\infty}(G)=5$.

— Bounding the Eviction Number of a Graph in Terms of its Independence Number  (2509.19535 - MacGillivray et al., 23 Sep 2025) in Section 2, immediately after Theorem 1 (Theorem \ref{small}); repeated as Question \ref{Question:Conclusion35} in Section Open Problems