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:
“Our young people are diseased with the theological problems of original sin, origin of evil, predestination, and the like. These never presented a practical difficulty to any man,—never darkened across any man’s road, who did not go out of his way to seek them. These are the soul’s mumps, and measles, and whooping- coughs, and those who have not caught them cannot describe their health or prescribe a cure. A simple mind will not know these enemies.”
—Ralph Waldo Emerson (1803–1882)
“I have said many times, and it is literally true, that there is absolutely nothing that could keep me in business, if my job were simply business to me. The human problems which I deal with every day—concerning employees as well as customers—are the problems that fascinate me, that seem important to me.”
—Hortense Odlum (1892–?)
“If we fail to meet our problems here, no one else in the world will do so. If we fail, the heart goes out of progressives throughout the world.”
—Eleanor Roosevelt (1884–1962)