article

Blockers and transversals

Authors:

C. BentzAuthors Info & Claims

Discrete Mathematics, Volume 309, Issue 13

Pages 4306 - 4314

https://doi.org/10.1016/j.disc.2009.01.006

Published: 01 July 2009 Publication History

Abstract

Given an undirected graph G=(V,E) with matching number @n(G), we define d-blockers as subsets of edges B such that @n((V,E@?B))@?@n(G)-d. We define d-transversals T as subsets of edges such that every maximum matching M has |M@?T|>=d. We explore connections between d-blockers and d-transversals. Special classes of graphs are examined which include complete graphs, regular bipartite graphs, chains and cycles and we construct minimum d-transversals and d-blockers in these special graphs. We also study the complexity status of finding minimum transversals and blockers in arbitrary graphs.

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Cited By

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https://dl.acm.org/doi/10.1007/s00453-023-01141-z
Lü HLi XZhang H(2023)On anti-Kekulé and s-restricted matching preclusion problemsJournal of Combinatorial Optimization10.1007/s10878-023-01034-545:4Online publication date: 28-Apr-2023
https://dl.acm.org/doi/10.1007/s10878-023-01034-5
Kim EMilanič MMonnot JPicouleau C(2022)Complexity and algorithms for constant diameter augmentation problemsTheoretical Computer Science10.1016/j.tcs.2021.05.020904:C(15-26)Online publication date: 15-Feb-2022
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Blockers and transversals
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
2. Theory of computation

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cover image Discrete Mathematics

Discrete Mathematics Volume 309, Issue 13

July, 2009

446 pages

ISSN:0012-365X

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Copyright © Elsevier B.V. © 2009.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 July 2009

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Cited By

Lucke FMann F(2024)Reducing Graph Parameters by Contractions and DeletionsAlgorithmica10.1007/s00453-023-01141-z86:3(825-851)Online publication date: 1-Mar-2024
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Lü HLi XZhang H(2023)On anti-Kekulé and s-restricted matching preclusion problemsJournal of Combinatorial Optimization10.1007/s10878-023-01034-545:4Online publication date: 28-Apr-2023
https://dl.acm.org/doi/10.1007/s10878-023-01034-5
Kim EMilanič MMonnot JPicouleau C(2022)Complexity and algorithms for constant diameter augmentation problemsTheoretical Computer Science10.1016/j.tcs.2021.05.020904:C(15-26)Online publication date: 15-Feb-2022
https://dl.acm.org/doi/10.1016/j.tcs.2021.05.020
Böck FPardey JPenso LRautenbach D(2022)Relating dissociation, independence, and matchingsDiscrete Applied Mathematics10.1016/j.dam.2022.07.012322:C(160-165)Online publication date: 15-Dec-2022
https://dl.acm.org/doi/10.1016/j.dam.2022.07.012
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Lucke FMann F(2022)Using Edge Contractions and Vertex Deletions to Reduce the Independence Number and the Clique NumberCombinatorial Algorithms10.1007/978-3-031-06678-8_30(412-424)Online publication date: 7-Jun-2022
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Zhang QGuan XPardalos P(2021)Maximum shortest path interdiction problem by upgrading edges on trees under weighted normJournal of Global Optimization10.1007/s10898-020-00958-079:4(959-987)Online publication date: 1-Apr-2021
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Laroche PMarchetti FMartin SNagih ARóka Z(2020)Multiple Bipartite Complete Matching Vertex Blocker ProblemDiscrete Optimization10.1016/j.disopt.2019.10055135:COnline publication date: 1-Feb-2020
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Cairo MMedvedev PAcosta NRizzi RTomescu A(2019)An Optimal O(nm) Algorithm for Enumerating All Walks Common to All Closed Edge-covering Walks of a GraphACM Transactions on Algorithms10.1145/334173115:4(1-17)Online publication date: 29-Jul-2019
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Zhang YZhou T(2017)On the edge insertion/deletion and controllability distance of linear structural systems2017 IEEE 56th Annual Conference on Decision and Control (CDC)10.1109/CDC.2017.8263985(2300-2305)Online publication date: 12-Dec-2017
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