Direct Product Primality Testing of Graphs is GI-hard
সংরক্ষণ করুন:
| প্রকাশিত: | arXiv.org (Mar 3, 2020), p. n/a |
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| প্রধান লেখক: | |
| অন্যান্য লেখক: | , |
| প্রকাশিত: |
Cornell University Library, arXiv.org
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | Citation/Abstract Full text outside of ProQuest |
| ট্যাগগুলো: |
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MARC
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| 001 | 2370796686 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 2370796686 | ||
| 045 | 0 | |b d20200303 | |
| 100 | 1 | |a Calderoni, Luca | |
| 245 | 1 | |a Direct Product Primality Testing of Graphs is GI-hard | |
| 260 | |b Cornell University Library, arXiv.org |c Mar 3, 2020 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a We investigate the computational complexity of the graph primality testing problem with respect to the direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both primality testing and a unique prime factorization can be determined in polynomial time for (finite) connected and nonbipartite graphs. The author states as an open problem how results on the direct product of nonbipartite, connected graphs extend to bipartite connected graphs and to disconnected ones. In this paper we partially answer this question by proving that the graph isomorphism problem is polynomial-time many-one reducible to the graph compositeness testing problem (the complement of the graph primality testing problem). As a consequence of this result, we prove that the graph isomorphism problem is polynomial-time Turing reducible to the primality testing problem. Our results show that connectedness plays a crucial role in determining the computational complexity of the graph primality testing problem. | |
| 653 | |a Isomorphism | ||
| 653 | |a Graphs | ||
| 653 | |a Complexity | ||
| 653 | |a Polynomials | ||
| 653 | |a Tensors | ||
| 700 | 1 | |a Margara, Luciano | |
| 700 | 1 | |a Moreno Marzolla | |
| 773 | 0 | |t arXiv.org |g (Mar 3, 2020), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2370796686/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2003.01591 |