Problems
The problem of finding the longest path or cycle that is an induced subgraph of a given hypercube graph is known as the snake-in-the-box problem.
Szymanski's conjecture concerns the suitability of a hypercube as an network topology for communications. It states that, no matter how one chooses a permutation connecting each hypercube vertex to another vertex with which it should be connected, there is always a way to connect these pairs of vertices by paths that do not share any directed edge.
Read more about this topic: Hypercube Graph
Famous quotes containing the word problems:
“Men decide far more problems by hate, love, lust, rage, sorrow, joy, hope, fear, illusion, or some other inward emotion than by reality, authority, any legal standard, judicial precedent, or statute.”
—Marcus Tullius Cicero (106–43 B.C.)
“It’s so easy during those first few months to think that the problems will never end. You feel as if your son will never sleep through the night, will always spit up food after eating, and will never learn to smile—even though you don’t know any adults or even older children who still act this way.”
—Lawrence Kutner (20th century)
“I am always glad to think that my education was, for the most part, informal, and had not the slightest reference to a future business career. It left me free and untrammeled to approach my business problems without the limiting influence of specific training.”
—Alice Foote MacDougall (1867–1945)