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| Counting K-4-subdivisions | |
| Miltzow, T; Schmidt, JM; Xia, MJ | |
| 2015 | |
| Source | DISCRETE MATHEMATICS
 |
| ISSN | 0012-365X |
| Volume | 338Issue:12Pages:2387-2392 |
| English Abstract | A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K-4. As a generalization, we ask for the minimum number of K-4-subdivisions that are contained in every 3-connected graph on n vertices. We prove that there are Omega(n(3)) such K-4-subdivisions and show that the order of this bound is tight for infinitely many graphs. We further investigate a better bound in dependence on m and prove that the computational complexity of the problem of counting the exact number of K-4-subdivisions is OP-hard. (C) 2015 Elsevier B.V. All rights reserved.; A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K-4. As a generalization, we ask for the minimum number of K-4-subdivisions that are contained in every 3-connected graph on n vertices. We prove that there are Omega(n(3)) such K-4-subdivisions and show that the order of this bound is tight for infinitely many graphs. We further investigate a better bound in dependence on m and prove that the computational complexity of the problem of counting the exact number of K-4-subdivisions is OP-hard. (C) 2015 Elsevier B.V. All rights reserved. |
| Indexed Type | SCI |
| Keyword | Counting K-4-subdivisions Cycles 3-connected Graphs |
| Department | FU Berlin, Berlin, Germany. TU Ilmenau, Ilmenau, Germany. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100864, Peoples R China. |
| Language | 英语 |
| WOS ID | WOS:000359955700026 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/17424 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Miltzow, T,Schmidt, JM,Xia, MJ. Counting K-4-subdivisions[J]. DISCRETE MATHEMATICS,2015,338(12):2387-2392. |
| APA | Miltzow, T,Schmidt, JM,&Xia, MJ.(2015).Counting K-4-subdivisions.DISCRETE MATHEMATICS,338(12),2387-2392. |
| MLA | Miltzow, T,et al."Counting K-4-subdivisions".DISCRETE MATHEMATICS 338.12(2015):2387-2392. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 1-s2.0-S0012365X1500（441KB） | 开放获取 | License | Application Full Text | |||
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