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 "exact complexity of exact four colorability"):
  Abstract: Let $M_k \seq \nats$ be a given set that consists of $k$ noncontiguous integers. Define $\exactcolor{M_k}$ to be the problem of determining whether $\chi(G)$, the chromatic number of a given graph $G$, equals one of the $k$ elements of the set $M_k$ exactly. In 1987, Wagner \cite{wag:j:min-max} proved that $\exactcolor{M_k}$ is $\bhlevel{2k}$-complete, where $M_k = \{6k+1, 6k+3, >..., 8k-1 \}$ and $\bhlevel{2k}$ is the $2k$th level of the boolean hierarchy over $\np$. In particular, for $k = 1$, it is DP-complete to determine whether $\chi(G) = 7$, where $\DP = \bhlevel{2}$. Wagner raised the question of how small the numbers in a $k$-element set $M_k$ can be chosen such that $\exactcolor{M_k}$ still is $\bhlevel{2k}$-complete. In particular, for $k = 1$, he asked if it is DP-complete to determine whether $\chi(G) = 4$. In this note, we solve this question of Wagner and determine the precise threshold $t \in \{4, 5, 6, 7\}$ for which the problem $\exactcolor{\{t\}}$ jumps from NP to DP-completeness: It is DP-complete to determine whether $\chi(G) = 4$, yet $\exactcolor{\{3\}}$ is in $\np$. More generally, for each $k \geq 1$, we show that $\exactcolor{M_k}$ is $\bhlevel{2k}$-complete for $M_k = \{3k+1, 3k+3,..., 5k-1\}$.

Includes members:
  Member "complexity of the exact domatic number problem and of the exact conveyor flow shop problem":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an improved exact algorithm for the domatic number problem")
  Member "unambiguous computation boolean hierarchies and sparse turing complete sets":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "complexity of the exact domatic number problem and of the exact conveyor flow shop problem")

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)