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 "not all equal and 1 in degree decompositions algorithmic complexity and applications"):
  Abstract: A Not-All-Equal (NAE) decomposition of a graph $G$ is a decomposition of the vertices of $G$ into two parts such that each vertex in $G$ has at least one neighbor in each part. Also, a 1-in-Degree decomposition of a graph $G$ is a decomposition of the vertices of $G$ into two parts $A$ and $B$ such that each vertex in the graph $G$ has exactly one neighbor in part $A$. Among our results, we show that for a given graph $G$, if $G$ does not have any cycle of length congruent to 2 mod 4, then there is a polynomial time algorithm to decide whether $G$ has a 1-in-Degree decomposition. In sharp contrast, we prove that for every $r$, $r\geq 3$, for a given $r$-regular bipartite graph $G$ determining whether $G$ has a 1-in-Degree decomposition is $ \mathbf{NP} $-complete. These complexity results have been especially useful in proving $ \mathbf{NP} $-completeness of various graph related problems for restricted classes of graphs. In consequence of these results we show that for a given bipartite 3-regular graph $G$ determining whether there is a vector in the null-space of the 0,1-adjacency matrix of $G$ such that its entries belong to $\{\pm 1,\pm 2\}$ is $\mathbf{NP} $-complete. Among other results, we introduce a new version of {Planar 1-in-3 SAT} and we prove that this version is also $ \mathbf{NP} $-complete. In consequence of this result, we show that for a given planar $(3,4)$-semiregular graph $G$ determining whether there is a vector in the null-space of the 0,1-incidence matrix of $G$ such that its entries belong to $\{\pm 1,\pm 2\}$ is $\mathbf{NP} $-complete.

Includes members:
  Member "polynomial time algorithms for weighted efficient domination problems in at free graphs and dually chordal graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on efficient domination for some classes of h free bipartite graphs")
  Member "the parameterized complexity of domination type problems and application to linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new algorithms for weighted k domination and total k domination problems in proper interval graphs")
  Member "algorithmic complexity of proper labeling problems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the algorithmic complexity of decomposing graphs into regular irregular structures")
  Member "efficient dominating and edge dominating sets for graphs and hypergraphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on efficient domination for some classes of h free bipartite graphs")
  Member "minimum weight triangulation is np hard":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "geometry and generation of a new graph planarity game")

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)