Social Structure Decomposition With Security Issue
Social structure decomposition has been a valuable research topic in the study of social networks, and it still has many unresolved problems. At the same time, an increasing number of people pays attention to the security issue that is worth considering and researching. With security consideration,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8742590/ |
| _version_ | 1818479657012428800 |
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| author | Wenshun Teng Huijuan Wang Hongling Chen Bin Liu |
| author_facet | Wenshun Teng Huijuan Wang Hongling Chen Bin Liu |
| author_sort | Wenshun Teng |
| collection | DOAJ |
| description | Social structure decomposition has been a valuable research topic in the study of social networks, and it still has many unresolved problems. At the same time, an increasing number of people pays attention to the security issue that is worth considering and researching. With security consideration, we study a new social structure decomposition problem that can be formulated as a minimization problem in graph theory as follows: given a social network with formulation as a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, partition the vertex set of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> into the minimum number of subsets, such that each subset induces an acyclic graph called a forest. This minimum number is called the vertex arboricity, denoted by <inline-formula> <tex-math notation="LaTeX">$va(G)$ </tex-math></inline-formula>. It is well known that the vertex arboricity <inline-formula> <tex-math notation="LaTeX">$va(G)\leq 3$ </tex-math></inline-formula> for each planar graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> in the graph theory. In this paper, we prove that for the planar graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, if no 3-cycle intersects a 4-cycle or no 3-cycle intersects a 5-cycle, then <inline-formula> <tex-math notation="LaTeX">$va(G)\leq 2$ </tex-math></inline-formula>. |
| first_indexed | 2024-12-10T11:13:39Z |
| format | Article |
| id | doaj.art-7f9aa3a9712f4febaed256f7b7c9457a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-10T11:13:39Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-7f9aa3a9712f4febaed256f7b7c9457a2022-12-22T01:51:18ZengIEEEIEEE Access2169-35362019-01-017827858279310.1109/ACCESS.2019.29240528742590Social Structure Decomposition With Security IssueWenshun Teng0Huijuan Wang1https://orcid.org/0000-0002-0171-2638Hongling Chen2Bin Liu3School of Mathematics and Statistics, Qingdao University, Qingdao, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao, ChinaSchool of Mathematical Sciences, Ocean University of China, Qingdao, ChinaSocial structure decomposition has been a valuable research topic in the study of social networks, and it still has many unresolved problems. At the same time, an increasing number of people pays attention to the security issue that is worth considering and researching. With security consideration, we study a new social structure decomposition problem that can be formulated as a minimization problem in graph theory as follows: given a social network with formulation as a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, partition the vertex set of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> into the minimum number of subsets, such that each subset induces an acyclic graph called a forest. This minimum number is called the vertex arboricity, denoted by <inline-formula> <tex-math notation="LaTeX">$va(G)$ </tex-math></inline-formula>. It is well known that the vertex arboricity <inline-formula> <tex-math notation="LaTeX">$va(G)\leq 3$ </tex-math></inline-formula> for each planar graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> in the graph theory. In this paper, we prove that for the planar graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, if no 3-cycle intersects a 4-cycle or no 3-cycle intersects a 5-cycle, then <inline-formula> <tex-math notation="LaTeX">$va(G)\leq 2$ </tex-math></inline-formula>.https://ieeexplore.ieee.org/document/8742590/Cyclesintersectingplanar graphvertex arboricity |
| spellingShingle | Wenshun Teng Huijuan Wang Hongling Chen Bin Liu Social Structure Decomposition With Security Issue IEEE Access Cycles intersecting planar graph vertex arboricity |
| title | Social Structure Decomposition With Security Issue |
| title_full | Social Structure Decomposition With Security Issue |
| title_fullStr | Social Structure Decomposition With Security Issue |
| title_full_unstemmed | Social Structure Decomposition With Security Issue |
| title_short | Social Structure Decomposition With Security Issue |
| title_sort | social structure decomposition with security issue |
| topic | Cycles intersecting planar graph vertex arboricity |
| url | https://ieeexplore.ieee.org/document/8742590/ |
| work_keys_str_mv | AT wenshunteng socialstructuredecompositionwithsecurityissue AT huijuanwang socialstructuredecompositionwithsecurityissue AT honglingchen socialstructuredecompositionwithsecurityissue AT binliu socialstructuredecompositionwithsecurityissue |