Hypergraph coloring up to condensation
نویسندگان
چکیده
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]. Mathematics Subject Classification: 05C80 (primary), 05C15 (secondary)
منابع مشابه
The condensation transition in random hypergraph 2-coloring
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 کاملA positive temperature phase transition in random hypergraph 2-coloring
Diluted mean-field models are graphical models in which the geometry of interactions is determined by a sparse random graph or hypergraph. Based on a non-rigorous but analytic approach called the “cavity method”, physicists have predicted that in many diluted mean-field models a phase transition occurs as the inverse temperature grows from 0 to ∞ [16]. In this paper we establish the existence a...
متن کاملColoring of Intuitionistic Fuzzy Directed Hypergraphs
A hypergraph is a set V of vertices and a set E of non-empty subsets of V , called hyperedges. Unlike graphs, hypergraphs can perform higher-order interactions in social and communication networks. Directed hypergraphs are much like directed graphs. Colors are used to distinguish the classes. Coloring a hypergraph H must assign atleast two different colors to the vertices of every hyperedge. Th...
متن کاملApproximate Hypergraph Coloring under Low-discrepancy and Related Promises
A hypergraph is said to be χ-colorable if its vertices can be colored with χ colors so that no hyperedge is monochromatic. 2-colorability is a fundamental property (called Property B) of hypergraphs and is extensively studied in combinatorics. Algorithmically, however, given a 2-colorable k-uniform hypergraph, it is NP-hard to find a 2-coloring miscoloring fewer than a fraction 2−k+1 of hypered...
متن کاملReducing uniformity in Khot-Saket hypergraph coloring hardness reductions
In a recent result, Khot and Saket [FOCS 2014] proved the quasi-NP-hardness of coloring a 2-colorable 12-uniform hypergraphwith 2 Ω(1) colors. This result was proved using a novel outer PCP verifier which had a strong soundness guarantee. In this note, we show that we can reduce the arity of their result by modifying their 12-query inner verifier to an 8-query inner verifier based on the hyperg...
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:
- CoRR
دوره abs/1508.01841 شماره
صفحات -
تاریخ انتشار 2015