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.)
“An interesting play cannot in the nature of things mean anything but a play in which problems of conduct and character of personal importance to the audience are raised and suggestively discussed.”
—George Bernard Shaw (1856–1950)
“I’m no good at being noble, but it doesn’t take much to see that the problems of three little people don’t amount to a hill of beans in this crazy world. Someday you’ll understand that.”
—Julius J. Epstein, U.S. screenwriter, Philip Epstein, screenwriter, Howard Koch, screenwriter, and Michael Curtiz. Rick Blaine (Humphrey Bogart)