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由E. Dauber<ref>E. Dauber, in ''Graph theory'', ed. F. Harary, Addison Wesley, (1969) p. 172.</ref>所提出的一个分区定理表明，对于边传递超图 <math>H=(X,E)</math>存在一个[[分区]]:<math>(X_1, X_2,\cdots,X_K)</math>对于顶点集 <math>X</math>使得由<math>X_k</math>生成的子超图<math>H_{X_k}</math>在<math>1\le k \le K</math>时是可传递的，并且使得<math>\sum_{k=1}^K r\left(H_{X_k} \right) = r(H)</math>，其中<math>r(H)</math>是 ''H''的秩。

由E. Dauber<ref>E. Dauber, in ''Graph theory'', ed. F. Harary, Addison Wesley, (1969) p. 172.</ref>所提出的一个定理表明，对于边传递超图 <math>H=(X,E)</math>存在一个'''划分 partition'''：<math>(X_1, X_2,\cdots,X_K)</math>对于顶点集 <math>X</math>使得由<math>X_k</math>生成的子超图<math>H_{X_k}</math>在<math>1\le k \le K</math>时是可传递的，并且使得<math>\sum_{k=1}^K r\left(H_{X_k} \right) = r(H)</math>，其中<math>r(H)</math>是 <math>H</math>的秩。

图分区(特别是超图分区)在集成电路设计<ref>{{Citation |title=Multilevel hypergraph partitioning: applications in VLSI domain |author=Karypis, G., Aggarwal, R., Kumar, V., and Shekhar, S. |journal=IEEE Transactions on Very Large Scale Integration (VLSI) Systems |date=March 1999 |volume=7 |issue=1 |pages=69–79 |doi=10.1109/92.748202 |postscript=.|citeseerx=10.1.1.553.2367 }}</ref> 和并行计算<ref>{{Citation |doi=10.1016/S0167-8191(00)00048-X |title=Graph partitioning models for parallel computing |author= Hendrickson, B., Kolda, T.G. |journal=Parallel Computing | year=2000 |volume=26 |issue=12 |pages=1519–1545 |postscript=.|url=https://digital.library.unt.edu/ark:/67531/metadc684945/ |type=Submitted manuscript }}</ref><ref>{{Cite conference |last1=Catalyurek |first1=U.V. |last2=Aykanat |first2=C. |title=A Hypergraph Model for Mapping Repeated Sparse Matrix-Vector Product Computations onto Multicomputers |conference=Proc. International Conference on Hi Performance Computing (HiPC'95) |year=1995}}</ref><ref>{{Citation |last1=Catalyurek |first1=U.V. |last2=Aykanat |first2=C. |title=Hypergraph-Partitioning Based Decomposition for Parallel Sparse-Matrix Vector Multiplication |journal=IEEE Transactions on Parallel and Distributed Systems |volume=10 |issue=7 |pages=673–693 |year=1999|doi=10.1109/71.780863 |postscript=. |citeseerx=10.1.1.67.2498 }}</ref>中有很多应用。在机器学习任务中，高效、可扩展的超图分区算法对于处理大规模超图也很重要。<ref name=hyperx>{{citation|last1=Huang|first1=Jin|last2=Zhang|first2=Rui|last3=Yu|first3=Jeffrey Xu|journal=Proceedings of the IEEE International Conference on Data Mining|title=Scalable Hypergraph Learning and Processing|year=2015}}</ref>

图划分(特别是超图划分)在集成电路设计 IC design <ref>{{Citation |title=Multilevel hypergraph partitioning: applications in VLSI domain |author=Karypis, G., Aggarwal, R., Kumar, V., and Shekhar, S. |journal=IEEE Transactions on Very Large Scale Integration (VLSI) Systems |date=March 1999 |volume=7 |issue=1 |pages=69–79 |doi=10.1109/92.748202 |postscript=.|citeseerx=10.1.1.553.2367 }}</ref> 和并行计算 parallel computing <ref>{{Citation |doi=10.1016/S0167-8191(00)00048-X |title=Graph partitioning models for parallel computing |author= Hendrickson, B., Kolda, T.G. |journal=Parallel Computing | year=2000 |volume=26 |issue=12 |pages=1519–1545 |postscript=.|url=https://digital.library.unt.edu/ark:/67531/metadc684945/ |type=Submitted manuscript }}</ref><ref>{{Cite conference |last1=Catalyurek |first1=U.V. |last2=Aykanat |first2=C. |title=A Hypergraph Model for Mapping Repeated Sparse Matrix-Vector Product Computations onto Multicomputers |conference=Proc. International Conference on Hi Performance Computing (HiPC'95) |year=1995}}</ref><ref>{{Citation |last1=Catalyurek |first1=U.V. |last2=Aykanat |first2=C. |title=Hypergraph-Partitioning Based Decomposition for Parallel Sparse-Matrix Vector Multiplication |journal=IEEE Transactions on Parallel and Distributed Systems |volume=10 |issue=7 |pages=673–693 |year=1999|doi=10.1109/71.780863 |postscript=. |citeseerx=10.1.1.67.2498 }}</ref>中有很多应用。此外，在机器学习任务中，高效、可扩展的超图划分算法对于处理大规模超图也很重要。<ref name=hyperx>{{citation|last1=Huang|first1=Jin|last2=Zhang|first2=Rui|last3=Yu|first3=Jeffrey Xu|journal=Proceedings of the IEEE International Conference on Data Mining|title=Scalable Hypergraph Learning and Processing|year=2015}}</ref>

==Theorems==

==Theorems==