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 "graph isomorphism color refinement and compactness"):
  Abstract: Color refinement is a classical technique used to show that two given graphs G and H are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph G amenable to color refinement if it succeeds in distinguishing G from any non-isomorphic graph H. Tinhofer (1991) explored a linear programming approach to Graph Isomorphism and defined compact graphs: A graph is compact if its fractional automorphisms polytope is integral. Tinhofer noted that isomorphism testing for compact graphs can be done quite efficiently by linear programming. However, the problem of characterizing and recognizing compact graphs in polynomial time remains an open question. #R##N#Our results are summarized below: #R##N#- We show that amenable graphs are recognizable in time O((n + m)logn), where n and m denote the number of vertices and the number of edges in the input graph. #R##N#- We show that all amenable graphs are compact. #R##N#- We study related combinatorial and algebraic graph properties introduced by Tinhofer and Godsil. The corresponding classes of graphs form a hierarchy and we prove that recognizing each of these graph classes is P-hard. In particular, this gives a first complexity lower bound for recognizing compact graphs.

Includes members:
  Member "graphs identified by logics with counting":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "what graph neural networks cannot learn depth vs width")
  Member "tight lower and upper bounds for the complexity of canonical colour refinement":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hypergraph isomorphism for groups with restricted composition factors")
  Member "dimension reduction via colour refinement":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "towards a practical k dimensional weisfeiler leman algorithm")
  Member "pebble games and linear equations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a survey on the expressive power of graph neural networks")

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.CC(Computational Complexity)