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 "graphs disjoint matchings and some inequalities"):
  Abstract: For $k \geq 1$ and a graph $G$ let $\nu_k(G)$ denote the size of a maximum $k$-edge-colorable subgraph of $G$. Mkrtchyan, Petrosyan and Vardanyan proved that $\nu_2(G)\geq \frac45\cdot |V(G)|$, $\nu_3(G)\geq \frac76\cdot |V(G)|$ for any cubic graph $G$ ~\cite{samvel:2010}. They were also able to show that if $G$ is a cubic graph, then $\nu_2(G)+\nu_3(G)\geq 2\cdot |V(G)|$ ~\cite{samvel:2014} and $\nu_2(G) \leq \frac{|V(G)| + 2\cdot \nu_3(G)}{4}$ ~\cite{samvel:2010}. In the first part of the present work, we show that the last two inequalities imply the first two of them. #R##N#Moreover, we show that $\nu_2(G) \geq \alpha \cdot \frac{|V(G)| + 2\cdot \nu_3(G)}{4} $, where #R##N#$\alpha=\frac{16}{17}$, if $G$ is a cubic graph, #R##N#$\alpha=\frac{20}{21}$, if $G$ is a cubic graph containing a perfect matching, #R##N#$\alpha=\frac{44}{45}$, if $G$ is a bridgeless cubic graph. #R##N#We also investigate the parameters $\nu_2(G)$ and $\nu_3(G)$ in the class of claw-free cubic graphs. We improve the lower bounds for $\nu_2(G)$ and $\nu_3(G)$ for claw-free bridgeless cubic graphs to $\nu_2(G)\geq \frac{35}{36}\cdot |V(G)|$ #R##N#($n \geq 48$), $\nu_3(G)\geq \frac{43}{45}\cdot |E(G)|$. On the basis of these inequalities we are able to improve the coefficient $\alpha$ for bridgeless claw-free cubic graphs. #R##N#In the second part of the work, we prove lower bounds for $\nu_k(G)$ in terms of $\frac{\nu_{k-1}(G)+\nu_{k+1}(G)}{2}$ for $k\geq 2$ and graphs $G$ containing at most $1$ cycle. We also present the corresponding conjectures for bipartite and nearly bipartite graphs.

Includes members:
  Member "on disjoint matchings in cubic graphs maximum 2 edge colorable and maximum 3 edge colorable subgraphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the fixed parameter tractability of the maximum 2 edge colorable subgraph problem")
  Member "beyond the vizing s bound for at most seven colors":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "maximum edge colorable subgraph and strong triadic closure parameterized by distance to low degree graphs")
  Member "on disjoint matchings in cubic graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the fixed parameter tractability of the maximum 2 edge colorable subgraph problem")
  Member "on parsimonious edge colouring of graphs with maximum degree three":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on maximum k edge colorable subgraphs of bipartite graphs")

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)