On bound graphs and poset operations

• Project/Area Number: 20540135
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokai University
• Principal Investigator: TSUCHIYA Morimasa Tokai University, 理学部, 教授 (00188583)
• Co-Investigator(Renkei-kenkyūsha): HARA Masao 東海大学, 理学部, 准教授 (10238165) ; MATSUI Yasuko 東海大学, 理学部, 准教授 (10264582) ; MATSUMOTO Satoshi 東海大学, 理学部, 准教授 (30307235)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 離散数学 / 応用数学 / 組合せ論 / グラフ理論 / 半順序集合 / strict-double-bound graph / strict-double-bound number / upper bound graph / double bound graph / forbidden subgraph

Research Abstract

We studied some kinds of bound graphs from the point of view of clique covers. Using properties of clique covers and posets, we characterized classes of upper bound graphs in terms of forbidden subgraphs.
And we introduced a concept of strict-double-bound numbers and gave strict-double-bound numbers of some families of graphs.

Research Products

• [Journal Article] On posets with double bound graphs which contain a star graphs with as an induced subgraphs (2010)
  • Author(s): K.Ogawa, S.Tgusari, M.Tsuchiya
  • Journal Title: Southeast Asian Bulletinof Mathematics 34 Pages: 1063-1075
  • Peer Reviewed
• [Journal Article] On distance two graphs of upper bound graphs (2010)
  • Author(s): K.Ogawa, S.Tgusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics 310 Pages: 3276-3277
  • Peer Reviewed
• [Journal Article] On distance two graphs of upper bound graphs (2010)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics Volume: 310 Pages: 3276-3277
  • Peer Reviewed
• [Journal Article] On posets with double bound graphs which contain a star graphs as an induced subgraph (2010)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Journal Title: Southeast Asian Bulletin of Mathematics Volume: 34 Pages: 1063-1075
  • Peer Reviewed
• [Journal Article] Note on upper bound graphs and forbidden subposets (2009)
  • Author(s): K.Ogawa, S.Tgusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics 309 Pages: 3659-3663
  • Peer Reviewed
• [Journal Article] On double bound graphs and forbidden subposets (2009)
  • Author(s): K.Ogawa, S.Tgusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics 309 Pages: 6353-6358
  • Peer Reviewed
• [Journal Article] On double bound graphs and forbidden subposets (2009)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics 309 Pages: 6353-6358
  • Peer Reviewed
• [Journal Article] Note on upper bound graphs and forbidden subposets (2009)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Journal Title: Discrete Mathematics 309 Pages: 3659-3663
  • Peer Reviewed
• [Journal Article] Note on upper bound graphs with forbidden subgraphs (2008)
  • Author(s): A.Kawamura, K.Ogawa, S.Tgusari, M.Tsuchiya
  • Journal Title: Advances and Applications in Discrete Mathematics 1 Pages: 215-226
  • Peer Reviewed
• [Journal Article] A note on some kinds of hereditary bound graphs (2008)
  • Author(s): H.Era, K.Ogawa, M.Tsuchiya
  • Journal Title: Utilitas Mathematics 77 Pages: 55-63
  • Peer Reviewed
• [Journal Article] A note on some kinds of hereditary bound graphs (2008)
  • Author(s): H. Era, K. Ogawa, M. Tsuchiya
  • Journal Title: Utilitas Mathematica 77 Pages: 55-63
  • Peer Reviewed
• [Journal Article] Note on upper bound graphs with forbidden subgraphs (2008)
  • Author(s): A. Kawamura, K. Ogawa S. Tgusari, M. Tsuchiya
  • Journal Title: Advances and Applications in Discrete Mathematics 1 Pages: 215-226
  • Peer Reviewed
• [Presentation] Cycles and p-competition graphs of digraphs without loops and symmetry arcs (2010)
  • Author(s): D.Kishida, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国,Hawaii
  • Year and Date: 2010-12-10
• [Presentation] On strict-DB-numbers of the Cartesian products of cycles (2010)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国,Hawaii
  • Year and Date: 2010-12-10
• [Presentation] On strict-DB-numbers of the Cartesian products of cycles (2010)
  • Author(s): K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshops on Discrete Mathematics
  • Place of Presentation: 米国, Hawaii
  • Year and Date: 2010-12-10
• [Presentation] Cycles and p-competition graphs of digraphs without loops and symmetry arcs (2010)
  • Author(s): D.Kishida, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshops on Discrete Mathematics
  • Place of Presentation: 米国, Hawaii
  • Year and Date: 2010-12-10
• [Presentation] Note on strict-double-bound-numbers of nearly complete graphs missing some dges (2010)
  • Author(s): K.Kanada, K.Kushima, K.Ogawa S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国,Hawaii
  • Year and Date: 2010-12-07
• [Presentation] On p-competition graphs of digraphs without loops and symmetric arcs (2010)
  • Author(s): Y.Kidokoro, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国,Hawaii
  • Year and Date: 2010-12-07
• [Presentation] On p-competition graphs of digraphs without loops and symmetric arcs (2010)
  • Author(s): Y.Kidokoro, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshops on Discrete Mathematics
  • Place of Presentation: 米国, Hawaii
  • Year and Date: 2010-12-07
• [Presentation] Note on strict-double-bound-numbers of nearly complete graphs missing some edges (2010)
  • Author(s): K.Kanada, K.Kushima, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 3^<rd> Pacific Workshops on Discrete Mathematics
  • Place of Presentation: 米国, Hawaii
  • Year and Date: 2010-12-07
• [Presentation] On strict-double-bound numbers (2010)
  • Author(s): K.Ogawa, R.Soejima, S.Tagusari, M.Tsuchiya
  • Organizer: Combanatorics 2010
  • Place of Presentation: イタリア,Verbania
  • Year and Date: 2010-06-29
• [Presentation] On strict-double bound numbers (2010)
  • Author(s): K.Ogawa, R.Soejima, S.Tagusari, M.Tsuchiya
  • Organizer: Combanatorics 2010
  • Place of Presentation: イタリア,Verbania
  • Year and Date: 2010-06-29
• [Presentation] On strict DB-numbers of the Cartesian products of star graphs and paths (2010)
  • Author(s): 小川健次郎,田鎖聡史,土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-24
• [Presentation] On strict double bound numbers of the Cartesian products of two cycles (2009)
  • Author(s): 小西翔大,小川健次郎,田鎖聡史,土屋守正
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2009-12-19
• [Presentation] On strict DB numbers (2009)
  • Author(s): 小西翔大,小川健次郎,田鎖聡史,土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] On strict double bound graphs (2009)
  • Author(s): S.Konishi, K.Ogawa, S.Tagusari, M.Tsuchiya
  • Organizer: 22^<nd> British Combinatorial Conference
  • Place of Presentation: 英国,St.Andrews
  • Year and Date: 2009-07-06
• [Presentation] Strict DB numberについて (2009)
  • Author(s): 小西翔太,小川健次郎,田鎖聡史,土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] Strict DB-graphについて (2009)
  • Author(s): 小川健次郎,田鎖聡史,土屋守正
  • Organizer: 日本数学
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] Strict DB-graph について (2009)
  • Author(s): 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] strict DB number について (2009)
  • Author(s): 小西翔太, 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] Two step graphのUB-graph性について (2008)
  • Author(s): 土屋守正,小川健次郎,田鎖聡史
  • Organizer: 日本数学会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] Two step graph の UB-graph性について (2008)
  • Author(s): 土屋守正, 小川健次郎田鎖聡史
  • Organizer: 日本数学会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] Upper bound 2-step graphについて, (2008)
  • Author(s): 土屋守正
  • Organizer: 純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
  • Place of Presentation: 電気通信大学
  • Year and Date: 2008-07-06
• [Presentation] Upper bound 2-step graph について (2008)
  • Author(s): 土屋守正
  • Organizer: 純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
  • Place of Presentation: 電気通信大学
  • Year and Date: 2008-07-06
• [Presentation] On upper bound graphs with graph operations (2008)
  • Author(s): 土屋守正
  • Organizer: Combinatorics 2008
  • Place of Presentation: Italy, Costermano
  • Year and Date: 2008-06-24
• [Presentation] On upper bound graphs with graph operations (2008)
  • Author(s): M. Tsuchiya
  • Organizer: Combinalorics 2008
  • Place of Presentation: Italy, Cosfermano
  • Year and Date: 2008-06-24
• [Book] 増補改訂版グラフ理論 (2010)
  • Author(s): 恵羅博,土屋守正
  • Total Pages: 238
  • Publisher: 産業図書
• [Book] 増補改訂版グラフ理論 (2010)
  • Author(s): 恵羅博, 土屋守正
  • Total Pages: 238
  • Publisher: 産業図書