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)
“Was it the double of my dream
The woman that by me lay
Dreamed, or did we halve a dream
Under the first cold gleam of day?”
—William Butler Yeats (1865–1939)
“See, there is a place by me where you shall stand on the rock; and while my glory passes by I will put you in a cleft of the rock, and I will cover you with my hand until I have passed by;
then I will take away my hand, and you shall see my back; but my face shall not be seen.””
—Bible: Hebrew, Exodus 33:21-23.