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 cycle of the machine is now coming to an end. Man has learned much in the hard discipline and the shrewd, unflinching grasp of practical possibilities that the machine has provided in the last three centuries: but we can no more continue to live in the world of the machine than we could live successfully on the barren surface of the moon.”
—Lewis Mumford (1895–1990)
“The worst feature of this double consciousness is, that the two lives, of the understanding and of the soul, which we lead, really show very little relation to each other; never meet and measure each other: one prevails now, all buzz and din; and the other prevails then, all infinitude and paradise; and, with the progress of life, the two discover no greater disposition to reconcile themselves.”
—Ralph Waldo Emerson (1803–1882)
“Between us, we cover all knowledge; he knows all that can be known and I know the rest.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)