Toward "good characterizations" of idealness of clutters

• Project/Area Number: 19540110
• 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: Yamagata University
• Principal Investigator: SAKUMA Tadashi Yamagata University, 地域教育文化学部, 准教授 (60323458)
• Project Period (FY): 2007 – 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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: clutter / ideality / excluded minor / MFMC-property / odd-hole recognition / path-parity / claw-free graph / pebble motion planning / the packing property / Matroid basis graph / Euclidean Distance Matrix

Research Abstract

In this study, we succeeded to characterize the ideality and the packing property for several classes of clutters which are corresponding to (a generalized classes of) the odd-holes of graphs by using the excluded clutter minors.

Research Products

• [Journal Article] N-flips in even triangulations on the torus and Dehn twists preserving monodromies (2011)
  • Author(s): Yusuke Higuchi, Atsushi Nakamoto, Kazuhiro Ota, Tadashi Sakuma
  • Journal Title: Discrete Mathematics 311(13) Pages: 1128-1135
  • Peer Reviewed
• [Journal Article] N-flips in even triangulations on the torus and Dehn twists preserving monodomies (2011)
  • Author(s): Yusuke Higuchi, Atsuhiro Nakamoto, Katsuhiro Ota, Tadashi Sakuma
  • Journal Title: Discrete Mathematics Volume: 311 Pages: 1128-1135
  • Peer Reviewed
• [Journal Article] The Positive circuits of oriented matroids with the packing property or idealness (2010)
  • Author(s): Kashiwaba Kenji, Sakuma Tadashi
  • Journal Title: Electronic Notes in Discrete Mathematics 36 Pages: 287-294
  • Peer Reviewed
• [Journal Article] On circular thin Lehman matrices (2010)
  • Author(s): Sakuma Tadashi, Shinohara Hidehiro
  • Journal Title: 応用数学合同研究集会報告集 Pages: 123-126
• [Journal Article] The positive circuits of oriented matroids with the packing property or idealness (2010)
  • Author(s): Kashiwabara Kenji, Tadashi Sakuma
  • Journal Title: Electronic Notes in Discrete Mathematics Volume: 36 Pages: 1287-1294
  • Peer Reviewed
• [Journal Article] Disjoint Even Cycles Packing (2009)
  • Author(s): Shuya Chiba, Shinya Fujita, Ken-ichi Kawarabayashi, Tadashi Sakuma
  • Journal Title: Electronic Notes in Discrete Mathematics 34 Pages: 113-119
  • Peer Reviewed
• [Journal Article] Colored Pebble Motion on Graphs (Extended Abstract) (2009)
  • Author(s): Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
  • Journal Title: Electronic Notes in Discrete Mathematics 34 Pages: 113-119
  • Peer Reviewed
• [Journal Article] Pebble Exchange on Graphs (Extended Abstract) (2009)
  • Author(s): Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
  • Journal Title: 第26回代数的組合せ論シンポジウム報告集 Pages: 126-132
• [Journal Article] Colored Pebble Motion on Graphs(Extended Abstract) (2009)
  • Author(s): Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
  • Journal Title: Electronic Notes in Discrete Mathematics 34 Pages: 185-189
  • Peer Reviewed
• [Journal Article] Pebble Exchange on Graphs(Extended Abstract) (2009)
  • Author(s): Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
  • Journal Title: 第26回代数的組合せ論シンポジウム報告集 Pages: 126-132
• [Journal Article] Determining the minimum rank of matroids whose basis graph is common (2008)
  • Author(s): Masahiro HACHIMORI, Hiroshi KURATA, Tadashi SAKUMA
  • Journal Title: Electronic Notes in Discrete Mathematics 31 Pages: 137-142
  • Peer Reviewed
• [Journal Article] Path-parity-solvability and its heredity (2008)
  • Author(s): Shinya FUJITA, Tadashi SAKUMA
  • Journal Title: Abstracts of the 20th Workshop on Topological Graph Theorey in Yokohama 1 Pages: 142-143
  • Peer Reviewed
• [Journal Article] On circulant thin Lehman matrices, Electronic Notes in Discrete Mathematics
  • Author(s): Sakuma Tadashi, Shinohara Hidehiro
  • Journal Title: Accepted
  • Peer Reviewed
• [Journal Article] olored Pebble Motion on Graphs, European Journal of Combinatorics
  • Author(s): Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
  • Journal Title: accepted
  • Peer Reviewed
• [Presentation] The positive circuits of oriented matroids with the packing property or idealness (2010)
  • Author(s): Tadashi Sakuma
  • Organizer: ISCO Hammamet : International Symposium on Combinatorial Optimization
  • Place of Presentation: Yasmine Hammamet at El Medina Mediterranea.
• [Presentation] The positive circuits of oriented matroids with the packing property or idealness (2010)
  • Author(s): Tadashi Sakuma
  • Organizer: ISCO Hammamet : International Symposium on Combinatorial Optimization
  • Place of Presentation: Yasmine Hammamet at El Medina Mediterranea
• [Presentation] The positive circuits of oriented matroids with the packing property or idealness. (2010)
  • Author(s): 佐久間雅
  • Organizer: ISCO Hammamet : International Symposium on Combinatorial Optimization
  • Place of Presentation: Yasmine Hammamet at El Medina Mediterranea.
• [Presentation] Colored Pebble Motion on Graphs (2009)
  • Author(s): 中上川友樹
  • Organizer: 離散数学とその応用に関する研究集会
  • Place of Presentation: 茨城大学
  • Year and Date: 2009-08-08
• [Presentation] Colored Pebble Motion on Graphs (2009)
  • Author(s): 佐久間雅
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 遊学館(山形県生涯学習センター)
  • Year and Date: 2009-06-26
• [Presentation] Disjoint Even Cycles Packing (2009)
  • Author(s): Shuya Chiba
  • Organizer: EuroComb 2009 : European Conference on Combinatorics, Graph Theory and Applications
  • Place of Presentation: University of Bordeauxl
• [Presentation] Colored Pebble Motion on Graphs(Extended Abstract) (2009)
  • Author(s): 中上川友樹
  • Organizer: EuroComb 2009 : European Conference on Combinatorics, Graph Theory and Applications
  • Place of Presentation: University of Bordeauxl
• [Presentation] Path-parity-solvability and its heredity (2008)
  • Author(s): Tadashi SAKUMA
  • Organizer: The 20th Workshop on Topological Graph Theorey in Yokohama
  • Place of Presentation: Yokohama National University, JAPAN
  • Year and Date: 2008-11-28
• [Presentation] Determining the minimum rank of matroids whose basis graph is common (2008)
  • Author(s): Tadashi SAKUMA
  • Organizer: Topological & Geometric Graph Theory (Dedicated to Hubert de Fraysseix on the Occasion of his 60th birthday)
  • Place of Presentation: Ecole Normale Superieure, Paris, FRANCE
  • Year and Date: 2008-05-21