Random article ( of 1062 ) Latest updates

User Tools

Site Tools


content:mathematics:cyclic_double_cover

Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

Cyclic double cover conjecture

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."

Source : Wikipedia

Put another way :

In every bridgeless graph one can find a family C of cycles such that each edge appears in exactly two cycles of C."

Source : North-Holland Mathematics Studies, Volume 115, 1985, Pages 1-12

The conjecture was first proposed in 1973 by mathematician George Szekeres. It's also sometimes known as the 'circular embedding conjecture'.

To date, the conjecture has neither been proved nor disproved.


Show another (random) article

Suggestions for corrections and ideas for articles are welcomed : Get in touch!


Further resources :

Do NOT follow this link or you will be banned from the site!

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK MAY 2024