# Hamiltonian Cycle

#### In a 54 vertex quartic graph.

By Vamshi Jandhyala in mathematics

December 31, 2020

While investigating whether a $54$ vertex *quartic* graph has a *Hamiltonian cycle* in the context of a recreational math problem, I came across this
theorem of Tutte, which says that every $4$-connected planar graph has a Hamiltonian cycle. I was unsure if a $54$ vertex *quartic* graph could be *planar*, so I googled “graph 54 vertices 108 edges”, lo and behold, here is the beautiful
**matchstick graph** and the Hamiltonian cycle that I found ðŸ˜Š.