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:
“Oh, life is a glorious cycle of song,
A medley of extemporanea;
And love is a thing that can never go wrong;
And I am Marie of Roumania.”
—Dorothy Parker (1893–1967)
“In a symbol there is concealment and yet revelation: here therefore, by silence and by speech acting together, comes a double significance.... In the symbol proper, what we can call a symbol, there is ever, more or less distinctly and directly, some embodiment and revelation of the Infinite; the Infinite is made to blend itself with the Finite, to stand visible, and as it were, attainable there. By symbols, accordingly, is man guided and commanded, made happy, made wretched.”
—Thomas Carlyle (1795–1881)
“There is nothing more poetic and terrible than the skyscrapers’ battle with the heavens that cover them. Snow, rain, and mist highlight, drench, or conceal the vast towers, but those towers, hostile to mystery and blind to any sort of play, shear off the rain’s tresses and shine their three thousand swords through the soft swan of the fog.”
—Federico García Lorca (1898–1936)