some basic definition to get you started it you’re not too much into it:
graph: a thing made of vertices(also called nodes) connected by edges.
path of a graph: if you traverse a part of graph visiting any(not necessarily all) vertex and edge you encounter exactly once, it’s called a path of that graph
cycle: cycle is basically path with your starting and end point being the same(hence the name)
now if you can visit every node of a graph exactly once(you can skip some edges, doesn’t matter) and come back to the same vertex you started from(aka cycle), that cycle is called a Hamiltonian cycle(named after William Rowan Hamilton, Irish mathematician). and the graph is a Hamiltonian graph.
so, this meme is basically replacing that Hamilton with this Hamilton(and the “cycle” from a mathematical concept to a race track).
also the race track is actually a Hamiltonian cycle(you can verify it using the definitions written above).
PS: another type of graph in a graph theory is an eulerian graph. which is a graph in which there exists a cycle(actually a circuit, but doesn’t matter much for this short overview) such that every edge is visited exactly once.
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