The colorful Helly theorem and general hypergraphs
نویسندگان
چکیده
منابع مشابه
The Colorful Helly Theorem and Colorful Resolutions of Ideals
We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I.Barany and its generalizations by G.Kalai and R.Meshulam translates to the algebraic side. Our main results are algebraic generalizations of these translations, which in particula...
متن کاملColorful Subhypergraphs in Kneser Hypergraphs
Using a Zq-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hy...
متن کاملColorful Subhypergraphs in Uniform Hypergraphs
There are several topological results ensuring in any properly colored graph the existence of a colorful complete bipartite subgraph, whose order is bounded from below by some topological invariants of some topological spaces associated to the graph. Meunier [Electron. J. Combin., 2014] presented the first colorful type result for uniform hypergraphs. In this paper, we give some new generalizat...
متن کاملApproximating the Colorful Carathéodory Theorem
Let P1, . . . , Pd+1 ⊂ R be d-dimensional point sets such that the convex hull of each Pi contains the origin. We call the sets Pi color classes, and we think of the points in Pi as having color i. A colorful choice is a set with at most one point from each color class. The colorful Carathéodory theorem guarantees the existence of a colorful choice whose convex hull contains the origin. So far,...
متن کاملOn Helly Hypergraphs with Variable Intersection Sizes
A hypergraphH is said to be p-Helly when every p-wise intersecting partial hypergraph H′ of H has nonempty total intersection. Such hypergraphs have been characterized by Berge and Duchet in 1975, and since then they have appeared in the literature in several contexts, especially for the case p = 2, in which they are referred simply as Helly hypergraphs. An interesting generalization of p-Helly...
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: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.09.029