human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "a further generalization of the colourful caratheodory theorem"
  Abstract: Given d+1 sets, or colours, \(\mathbf{S}_{1},\mathbf{S}_{2},\ldots,\mathbf{S}_{d+1}\) of points in \({\mathbb{R}}^{d}\), a colourful set is a set \(S \subseteq \bigcup _{i}\mathbf{S}_{i}\) such that \(\vert S \cap \mathbf{S}_{i}\vert \leq 1\) for \(i = 1,\ldots,d + 1\). The convex hull of a colourful set S is called a colourful simplex. Barany’s colourful Caratheodory theorem asserts that if the origin 0 is contained in the convex hull of S i for \(i = 1,\ldots,d + 1\), then there exists a colourful simplex containing 0. The sufficient condition for the existence of a colourful simplex containing 0 was generalized to 0 being contained in the convex hull of \(\mathbf{S}_{i} \cup \mathbf{S}_{j}\) for 1≤i<j≤d+1 by Arocha etal. and by Holmsen etal. We further generalize the sufficient condition and obtain new colourful Caratheodory theorems. We also give an algorithm to find a colourful simplex containing 0 under the generalized condition. In the plane an alternative, and more general, proof using graphs is given. In addition, we observe that any condition implying the existence of a colourful simplex containing 0 actually implies the existence of min i |S i |such simplices.

Connected through hyperedge HE-1 (induced by source paper "computational aspects of the colorful caratheodory theorem"):
  with members:
    - "the rainbow at the end of the line a ppad formulation of the colorful carath eodory theorem with applications"
    - "colorful linear programming nash equilibrium and pivots"
    - "approximating tverberg points in linear time for any fixed dimension"

Connected through hyperedge HE-2 (induced by source paper "colorful linear programming nash equilibrium and pivots"):
  with members:
    - "oriented euler complexes and signed perfect matchings"
    - "reducibility among fractional stability problems"
    - "settling the complexity of computing two player nash equilibria"

Question: Please tell me which class the center node 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.CG(Computational Geometry)