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:
“Those great ideas which come to you in your sleep just before you awake in morning, those solutions to the world’s problems which, in the light of day, turn out to be duds of the puniest order, couldn’t they be put to some use, after all?”
—Robert Benchley (1889–1945)
“The mother’s and father’s attitudes toward the child correspond to the child’s own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
—Erich Fromm (1900–1980)
“In many ways, life becomes simpler [for young adults]. . . . We are expected to solve only a finite number of problems within a limited range of possible solutions. . . . It’s a mental vacation compared with figuring out who we are, what we believe, what we’re going to do with our talents, how we’re going to solve the social problems of the globe . . .and what the perfect way to raise our children will be.”
—Roger Gould (20th century)