منابع مشابه
Hypergraph coloring up to condensation
Improving a result of Dyer, Frieze and Greenhill [Journal of Combinatorial Theory, Series B, 2015], we determine the q-colorability threshold in random k-uniform hypergraphs up to an additive error of ln2+εq , where limq→∞ εq = 0. The new lower bound on the threshold matches the “condensation phase transition” predicted by statistical physics considerations [Krzakala et al., PNAS 2007]. Mathema...
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For many random constraint satisfaction problems such as random satisfiability or random graph or hypergraph coloring, the best current estimates of the threshold for the existence of solutions are based on the first and the second moment method. However, in most cases these techniques do not yield matching upper and lower bounds. Sophisticated but non-rigorous arguments from statistical mechan...
متن کاملHardness for Hypergraph Coloring
We show that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 2(logN) 1/10−o(1) colors, where N is the number of vertices. There has been much focus on hardness of hypergraph coloring recently. In [17], Guruswami, H̊astad, Harsha, Srinivasan and Varma showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 22Ω( √ log logN) colors. Their result is obtain...
متن کاملApproximate Hypergraph Coloring
A coloring of a hypergraph is a mapping of vertices to colors such that no hyperedge is monochromatic. We are interested in the problem of coloring 2-colorable hypergraphs. For the special case of graphs (hypergraphs of dimension 2) this can easily be done in linear time. The problem for general hypergraphs is much more difficult since a result of Lovász implies that the problem is NP-hard even...
متن کاملTesting Hypergraph Coloring
In this paper we initiate the study of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is “far away” from the property. We prove that the fundamental problem of `-colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph. We present a testing algorithm ...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20824