Profiles of Separations: in Graphs, Matroids, and Beyond

被引:0
作者
Reinhard Diestel
Fabian Hundertmark
Sahar Lemanczyk
机构
[1] Universität Hamburg,Mathematisches Seminar
来源
Combinatorica | 2019年 / 39卷
关键词
05C05; 05C40; 05C83; 05B35; 06A07;
D O I
暂无
中图分类号
学科分类号
摘要
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem for more general combina- torial structures, which has further applications.
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页码:37 / 75
页数:38
相关论文
共 32 条
  • [1] Carmesin J.(2014)k-Blocks: a connectivity invariant for graphs SIAM J. Discrete Math. 28 1876-1891
  • [2] Diestel R.(2016)Canonical tree-decompositions of finite graphs I. Existence and algorithms J. Combin. Theory Ser. B 116 1-24
  • [3] Hamann M.(2016)Canonical tree-decompositions of finite graphs II. Essential parts J. Combin. Theory Ser. B 118 268-283
  • [4] Hundertmark F.(2014)Connectivity and tree structure in finite graphs Combinatorica 34 1-35
  • [5] Carmesin J.(2018)Abstract separation systems Order 35 157-170
  • [6] Diestel R.(2018)Tree sets Order 35 171-192
  • [7] Hamann M.(2017)Duality theorem for blocks and tangles in graphs SIAM J. Discrete Math. 31 1514-1528
  • [8] Hundertmark F.(2006)Obstructions to branch- decomposition of matroids J. Combin. Theory (Series B) 96 560-570
  • [9] Carmesin J.(2009)Tangles, tree-decompositions and grids in matroids J. Combin. Theory (Series B) 99 657-667
  • [10] Diestel R.(1961)Multi-terminal network flows J. Soc. Ind. Appl. Math. 9 551-570