Similarities between the blocking and anti-blocking polyhedra

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400185
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yamagata University
• Principal Investigator: Sakuma Tadashi 山形大学, 地域教育文化学部, 准教授 (60323458)
• Co-Investigator(Kenkyū-buntansha): 柏原 賢二 東京大学, 大学院総合文化研究科, 助教 (70282514)
• Co-Investigator(Renkei-kenkyūsha): HACHIMORI Masahiro 筑波大学, システム情報系, 准教授 (00344862) ; NAKAMURA Masataka 東京大学, 大学院総合文化研究科, 准教授 (90155854)
• Research Collaborator: SHINOHARA Hidehiro
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: Ideal clutter / Packing Property / MFMC Property / Tutte Polynomial / Chord Diagram / safe set / network majority

Outline of Final Research Achievements

1): We give a scheme to attack the following conjecture proposed by Cornuejols, Guenin and Margot:"Every ideal minimally non-packing clutter has a transversal of size 2." Moreover, we show that the clutter of a combinatorial affine plane does not have any ideal minimally non-packing clutter of blocking number at least 3. 2): We prove that the chord expansion number equals the value of the Tutte polynomial at the point (2,-1) for its corresponding interlace graph. 3): A safe set of a graph G=(V,E) is a non-empty subset S of V such that for every component A of G[S] and every component B of G[V-S], we have |A|+1>|B| whenever there exists an edge of G between A and B. We give several graph theoretical properties of this concept. Furthermore we evaluate computational complexities of the problem of computing the minimum weight of a safe set on several graph classes.

Free Research Field

組合せ最適化、離散数学