A Helly theorem for convexity in graphs
نویسندگان
چکیده
منابع مشابه
Helly theorems for 3-Steiner and 3-monophonic convexity in graphs
A family C of sets has the Helly property if any subfamily C′, whose elements are pairwise intersecting, has non-empty intersection. Suppose C is a non-empty family of subsets of a finite set V . The Helly number h(C) of C is the smallest positive integer n such that every subfamily C′ of C with |C′| ≥ n and which intersects n-wise has non-empty intersection. In this paper we consider the famil...
متن کاملA helly type theorem for hypersurfaces
Let r be a commutative field (finite or infinite) and let P = P(n, r) be the n-dimensional projective space over ZY Then every point x E P can be expressed by n + 1 homogene coordinates x = (x,,..., x,), not all zero and (x0,..., x,) = @x0,..., Ax,) for OflET. By a hypersurface of degree d we simply mean the set of all points x E P with p(x) = 0, where p(x) is a homogenous polynomial of degree ...
متن کاملA Helly theorem in weakly modular space
The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as...
متن کاملOn a Theorem of E. Helly
E. Helly’s theorem asserts that any bounded sequence of monotone real functions contains a pointwise convergent subsequence. We reprove this theorem in a generalized version in terms of monotone functions on linearly ordered sets. We show that the cardinal number responsible for this generalization is exactly the splitting number. We also show that a positive answer to a problem of S. Saks is o...
متن کاملBiclique-Helly Graphs
A graph is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly graphs, leading to polynomial time recognition algorithms. In addition, we relate biclique-Helly graphs to the classes of clique-Helly, disk-Helly and neighborhood-Helly graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90021-9