Three-vertex-constrained bipancyclicity of hypercubes

Pancyclicity and bipancyclicity are classical properties in graph theory, ensuring the existence of cycles of all admissible lengths in general and bipartite graphs. These notions were strengthened by vertex-(bi)pancyclicity, which requires cycles of every length to contain a prescribed vertex. However, prior work has focused almost exclusively on single-vertex constraints, leaving the multi-vertex setting largely unexplored. Motivated by this gap, we introduce and study k-vertex-constrained (bi)pancyclicity, which demands cycles of all admissible lengths to pass through an arbitrary set of k specified vertices. This paper presents Qn is 3-vertex-constrained bipancyclic if n ≥ 5.