A Counterexample to Wegner's Conjecture on Good Covers
نویسنده
چکیده
In 1975 Wegner conjectured that the nerve of every finite good cover in R is d-collapsible. We disprove this conjecture. A good cover is a collection of open sets in R such that the intersection of every subcollection is either empty or homeomorphic to an open d-ball. A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at most d − 1 which is contained in a unique maximal face.
منابع مشابه
On the oriented perfect path double cover conjecture
An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that ...
متن کاملCovers in Uniform Intersecting Families and a Counterexample to a Conjecture of Lovász
We discuss the maximum size of uniform intersecting families with covering number at least . Among others, we construct a large k-uniform intersecting family with covering number k, which provides a counterexample to a conjecture of Lov asz. The construction for odd k can be visualized on an annulus, while for even k on a Mobius band.
متن کاملFinite planar emulators for K4, 5-4K2 and K1, 2, 2, 2 and Fellows' Conjecture
In 1988 Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K4,5 − 4K2. Archdeacon [Dan Archdeacon, Two graphswithout planar covers, J. Graph Theory, 41 (4) (2002) 318–326] showed that K4,5−4K2 does not admit a finite planar cover; thusK4,5−4K2 provides a counterexample to Fellows’...
متن کاملA 64-Dimensional Counterexample to Borsuk's Conjecture
Bondarenko’s 65-dimensional counterexample to Borsuk’s conjecture contains a 64-dimensional counterexample. It is a two-distance set of 352 points.
متن کاملOn the Construction of a C-counterexample to the Hamiltonian Seifert Conjecture in R
We outline the construction of a proper C2-smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete & Computational Geometry
دوره 47 شماره
صفحات -
تاریخ انتشار 2012