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.)
“The problems of victory are more agreeable than the problems of defeat, but they are no less difficult.”
—Winston Churchill (1874–1965)
“I respect guilt. It is a dangerous but sometimes useful beast. The guilt that made me want to solve all my children’s problems meant trouble. The guilt that made me question my role in our mother-daughter squabbles proved helpful. Yes, I care about my kids’ problems, and I long to make suggestions. But these days I wait for children to ask for help, and I give it sparingly. Some things can’t be fixed, and I tell them so.”
—Susan Ferraro (20th century)