article

Submodular partition functions

Authors:

Omid Amini,

Frédéric Mazoit,

Nicolas Nisse,

Stéphan ThomasséAuthors Info & Claims

Discrete Mathematics, Volume 309, Issue 20

Pages 6000 - 6008

https://doi.org/10.1016/j.disc.2009.04.033

Published: 01 October 2009 Publication History

Abstract

Adapting the method introduced in Graph Minors X, we propose a new proof of the duality between the bramble number of a graph and its tree-width. Our approach is based on a new definition of submodularity on partition functions which naturally extends the usual one on set functions. The proof does not rely on Menger's theorem, and thus generalises the original one. It thus provides a dual for matroid tree-width. One can also derive all known dual notions of other classical width-parameters from it.

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Cited By

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Mescoff GPaul CThilikos D(2023)The mixed search game against an agile and visible fugitive is monotoneDiscrete Mathematics10.1016/j.disc.2023.113345346:4Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1016/j.disc.2023.113345
Bożyk ŁDefrain OOkrasa KPilipczuk M(2022)On objects dual to tree-cut decompositionsJournal of Combinatorial Theory Series B10.1016/j.jctb.2022.07.009157:C(401-428)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.jctb.2022.07.009
Diestel ROum S(2019)Tangle-Tree Duality: In Graphs, Matroids and BeyondCombinatorica10.1007/s00493-019-3798-539:4(879-910)Online publication date: 1-Aug-2019
https://dl.acm.org/doi/10.1007/s00493-019-3798-5
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Submodular partition functions
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
2. Theory of computation

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Published In

Discrete Mathematics Volume 309, Issue 20

October, 2009

253 pages

ISSN:0012-365X

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 October 2009

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Mescoff GPaul CThilikos D(2023)The mixed search game against an agile and visible fugitive is monotoneDiscrete Mathematics10.1016/j.disc.2023.113345346:4Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1016/j.disc.2023.113345
Bożyk ŁDefrain OOkrasa KPilipczuk M(2022)On objects dual to tree-cut decompositionsJournal of Combinatorial Theory Series B10.1016/j.jctb.2022.07.009157:C(401-428)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.jctb.2022.07.009
Diestel ROum S(2019)Tangle-Tree Duality: In Graphs, Matroids and BeyondCombinatorica10.1007/s00493-019-3798-539:4(879-910)Online publication date: 1-Aug-2019
https://dl.acm.org/doi/10.1007/s00493-019-3798-5
Basu Roy SLakshmanan LLiu RSellis TDavidson SIves Z(2015)From Group Recommendations to Group FormationProceedings of the 2015 ACM SIGMOD International Conference on Management of Data10.1145/2723372.2749448(1603-1616)Online publication date: 27-May-2015
https://dl.acm.org/doi/10.1145/2723372.2749448
Marx D(2013)Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive QueriesJournal of the ACM10.1145/253592660:6(1-51)Online publication date: 1-Nov-2013
https://dl.acm.org/doi/10.1145/2535926

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Recommendations

The relative clique-width of a graph

Maximizing k-Submodular Functions and Beyond

Submodular functions: from discrete to continuous domains

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