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 "on the number of types in sparse graphs"):
  Abstract: We prove that for every class of graphs $\mathcal{C}$ which is nowhere dense, as defined by Nesetril and Ossona de Mendez, and for every first order formula $\phi(\bar x,\bar y)$, whenever one draws a graph $G\in \mathcal{C}$ and a subset of its nodes $A$, the number of subsets of $A^{|\bar y|}$ which are of the form $\{\bar v\in A^{|\bar y|}\, \colon\, G\models\phi(\bar u,\bar v)\}$ for some valuation $\bar u$ of $\bar x$ in $G$ is bounded by $\mathcal{O}(|A|^{|\bar x|+\epsilon})$, for every $\epsilon>0$. This provides optimal bounds on the VC-density of first-order definable set systems in nowhere dense graph classes. #R##N#We also give two new proofs of upper bounds on quantities in nowhere dense classes which are relevant for their logical treatment. Firstly, we provide a new proof of the fact that nowhere dense classes are uniformly quasi-wide, implying explicit, polynomial upper bounds on the functions relating the two notions. Secondly, we give a new combinatorial proof of the result of Adler and Adler stating that every nowhere dense class of graphs is stable. In contrast to the previous proofs of the above results, our proofs are completely finitistic and constructive, and yield explicit and computable upper bounds on quantities related to uniform quasi-wideness (margins) and stability (ladder indices).

Includes members:
  Member "characterising bounded expansion by neighbourhood complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a general kernelization technique for domination and independence problems in sparse classes")
  Member "polynomial kernels and wideness properties of nowhere dense graph classes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a general kernelization technique for domination and independence problems in sparse classes")
  Member "neighborhood complexity and kernelization for nowhere dense classes of graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the parameterized complexity of reconfiguration of connected dominating sets")
  Member "kernelization and sparseness the case of dominating set":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "domination above r independence does sparseness help")
  Member "deciding first order properties of nowhere dense graphs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "hitting topological minors is fpt")
  Member "homomorphism preservation on quasi wide classes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "empirical evaluation of approximation algorithms for generalized graph coloring and uniform quasi wideness")

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)