human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "chasing the k colorability threshold"):
  Abstract: Over the past decade, physicists have developed deep but non-rigorous techniques for studying phase transitions in discrete structures. Recently, their ideas have been harnessed to obtain improved rigorous results on the phase transitions in binary problems such as random $k$-SAT or $k$-NAESAT (e.g., Coja-Oghlan and Panagiotou: STOC 2013). However, these rigorous arguments, typically centered around the second moment method, do not extend easily to problems where there are more than two possible values per variable. The single most intensely studied example of such a problem is random graph $k$-coloring. Here we develop a novel approach to the second moment method in this problem. This new method, inspired by physics conjectures on the geometry of the set of $k$-colorings, allows us to establish a substantially improved lower bound on the $k$-colorability threshold. The new lower bound is within an additive $2\ln 2+o_k(1)\approx 1.39$ of a simple first-moment upper bound and within $2\ln 2-1+o_k(1)\approx 0.39$ of the physics conjecture. By comparison, the best previous lower bound left a gap of about $2+\ln k$, unbounded in terms of the number of colors [Achlioptas, Naor: STOC 2004].

Includes members:
  Member "the condensation phase transition in random graph coloring":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "information theoretic thresholds from the cavity method")
  Member "on the chromatic number of a random hypergraph":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "information theoretic thresholds from the cavity method")
  Member "catching the k naesat threshold":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "general bounds on satisfiability thresholds for random csps via fourier analysis")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DM(Discrete Mathematics)