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:
“Only mediocrities progress. An artist revolves in a cycle of masterpieces, the first of which is no less perfect than the last.”
—Oscar Wilde (1854–1900)
“We are, I know not how, double within ourselves, with the result that we do not believe what we believe, and we cannot rid ourselves of what we condemn.”
—Michel de Montaigne (1533–1592)
“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)