In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly twice. For instance, for any polyhedral graph, the faces of a convex polyhedron that represents the graph provide a double cover of the graph: each edge belongs to exactly two faces.
It is an unsolved problem, posed by George Szekeres and Paul Seymour and known as the cycle double cover conjecture, whether every bridgeless graph has a cycle double cover. The conjecture can equivalently be formulated in terms of graph embeddings, and in that context is also known as the circular embedding conjecture.
Read more about Cycle Double Cover: Formulation, Reduction To Snarks, Reducible Configurations, Circular Embedding Conjecture, Stronger Conjectures and Related Problems
Famous quotes containing the words cycle, double and/or cover:
“The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a cycle transmission as he does at the top of a mountain or in the petals of a flower.”
—Robert M. Pirsig (b. 1928)
“The obsession with suicide is characteristic of the man who can neither live nor die, and whose attention never swerves from this double impossibility.”
—E.M. Cioran (b. 1911)
“You may call a jay a bird. Well, so he is, in a measure—because he’s got feathers on him, and don’t belong to no church, perhaps; but otherwise he is just as much a human as you be. And I’ll tell you for why. A jay’s gifts and instincts, and feelings, and interests, cover the whole ground. A jay hasn’t got any more principle than a Congressman.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)