On relations of bound graphs and order ideals

2013 Fiscal Year Final Research Report

• Project/Area Number: 23540161
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokai University
• Principal Investigator: TSUCHIYA Morimasa 東海大学, 理学部, 教授 (00188583)
• Co-Investigator(Kenkyū-buntansha): 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): 2011 – 2013
• Keywords: 応用数学 / 離散数学 / グラフ理論

Research Abstract

We studied some kinds of bound graphs from the point of view of clique covers, order ideals and intervals. Using properties of sets of maximal elements and sets of minimal elements of posets, we obtain some properties of strict-semi-bound graphs.
And we consider strict-double-bound numbers which are the number of isolated vertices with clique covers and estimate strict-double-bound numbers of some families of graphs.

Research Products

• [Journal Article] On strict-double-bound numbers of complete graphs missing four edges (2013)
  • Author(s): Kenjiro Ogawa, Keisuke Kanada, Kanosa Kushima, Satoshi Tagusari, Morimasa Tsuchiya
  • Journal Title: Bulletin of the Institute of Combinatorics and its Appilcations Volume: 68 Pages: 79-89
  • Peer Reviewed
• [Journal Article] On strict-double-bound numbers of spiders and ladders (2013)
  • Author(s): Syota Konishi, Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Journal Title: Ars Combinatorica Volume: 108 Pages: 249-255
  • Peer Reviewed
• [Journal Article] Note on strict-double-bound numbers of paths: cycles, and wheels (2012)
  • Author(s): Shota Konishi, Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Journal Title: JCMCC Volume: 83 Pages: 205-210
  • Peer Reviewed
• [Journal Article] Note on strict-double-bound numbers of nearly complete graphs missing some edges (2012)
  • Author(s): Kenjiro Ogawa, Ryoko Soejima, Satoshi Tagusari, Morimasa Tsuchiya
  • Journal Title: Discrete Mathematics Volume: 312 Pages: 584-587
  • Peer Reviewed
• [Journal Article] A polynomial-time perfect sampler for the Q-Ising with a vertex-independent noise (2011)
  • Author(s): Masaki Yamamoto, Shuji Kijima, Yasuko Matsui
  • Journal Title: Journal of Combinatorial Optimization Volume: 22 Pages: 3, 392-408
  • Peer Reviewed
• [Presentation] グラフ演算とsDB グラフについて (2013)
  • Author(s): 後藤佳弘, 池田一孝, 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: 2013-12-21
• [Presentation] Upper-bound graph について (2013)
  • Author(s): 川谷元, 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: 2013-12-20
• [Presentation] On strict-double-bound numbers of graphs and graph operations graphs and graph operations (2013)
  • Author(s): Gen Kawatani, Kenjito Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: The 25-th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2013-11-20
• [Presentation] On strict-semi- bound graphs of posets (2013)
  • Author(s): Morimasa Tsuchiya, Kenjiro Ogawa, Satoshi Tagusari
  • Organizer: Seventh Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications
  • Place of Presentation: スロバキア, コシチェ
  • Year and Date: 2013-07-09
• [Presentation] Strict-semi-bound graph について (2013)
  • Author(s): 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-20
• [Presentation] On p-competition graphs and spider graphs (2012)
  • Author(s): Kyohei Nakada, Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: 4th Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国, ハワイ
  • Year and Date: 2012-11-27
• [Presentation] On strict-semi- bound graphs of posets (2012)
  • Author(s): Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: 4th Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国, ハワイ
  • Year and Date: 2012-11-27
• [Presentation] On strict-double-bound numbers of trees (2012)
  • Author(s): Yuhei Shiraki, Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: 4th Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国, ハワイ
  • Year and Date: 2012-11-27
• [Presentation] On strict-double- bound numbers of graphs and graph operations (2012)
  • Author(s): Gen Kawatani, Yoshihiro Goto, Kenjiro Ogawa, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: 4th Pacific Workshop on Discrete Mathematics
  • Place of Presentation: 米国, ハワイ
  • Year and Date: 2012-11-27
• [Presentation] On strict-double-bound numbers of spiders, ladders, and pans (2012)
  • Author(s): Morimasa Tsuchiya, Kenjiro Ogawa, Keisuke Kanada, Shota Konishi, Kanosa Kushima, Satoshi Tagusari
  • Organizer: Combnatorics 2012
  • Place of Presentation: イタリア, ペルージャ
  • Year and Date: 2012-09-10
• [Presentation] Double Starのp-competition numberについて (2011)
  • Author(s): 仲田京平, 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 第23回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2011-11-26
• [Presentation] Double Star のstrict-DB number について (2011)
  • Author(s): 白木由平, 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 第23回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2011-11-26
• [Presentation] 4辺除去をした完全グラフのsDB number について (2011)
  • Author(s): 金田圭介, 串間花乃咲, 小川健次郎, 田鎖聡史, 土屋守正
  • Organizer: 日本数学会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-28
• [Presentation] On strict-double-bound numbers of complete graphs missing four edges (2011)
  • Author(s): Kenjiro Ogawa, Keisuke Kanada, Kanosa Kushima, Satoshi Tagusari, Morimasa Tsuchiya
  • Organizer: 23rd British Combinatorial Conference
  • Place of Presentation: 英国, University of Exeter
  • Year and Date: 2011-07-04