research-article

Nearly complete graphs decomposable into large induced matchings and their applications

Authors:

Benny SudakovAuthors Info & Claims

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

Pages 1079 - 1090

https://doi.org/10.1145/2213977.2214074

Published: 19 May 2012 Publication History

Abstract

We describe two constructions of (very) dense graphs which are edge disjoint unions of large induced matchings. The first construction exhibits graphs on N vertices with (^N₂)-o(N²) edges, which can be decomposed into pairwise disjoint induced matchings, each of size N^1-o(1). The second construction provides a covering of all edges of the complete graph K_N by two graphs, each being the edge disjoint union of at most N^2-δ induced matchings, where δ>0.076. This disproves (in a strong form) a conjecture of Meshulam, substantially improves a result of Birk, Linial and Meshulam on communicating over a shared channel, and (slightly) extends the analysis of Hastad and Wigderson of the graph test of Samorodnitsky and Trevisan for linearity. Additionally, our constructions settle a combinatorial question of Vempala regarding a candidate rounding scheme for the directed Steiner tree problem.

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Cited By

Behnezhad SGhafari A(2024)Fully Dynamic Matching and Ordered Ruzsa-Szemerédi Graphs2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00027(314-327)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00027
Alman JBłasiok J(2023)Matrix Multiplication and Number on the Forehead CommunicationProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.16(1-23)Online publication date: 17-Jul-2023
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Assadi S(2023)Recent Advances in Multi-Pass Graph Streaming Lower BoundsACM SIGACT News10.1145/3623800.362380854:3(48-75)Online publication date: 11-Sep-2023
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Index Terms

Nearly complete graphs decomposable into large induced matchings and their applications
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics

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cover image ACM Conferences

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

May 2012

1310 pages

ISBN:9781450312455

DOI:10.1145/2213977

General Chair:
Howard Karloff
AT&T Labs--Research
,
Program Chair:
Toniann Pitassi
University of Toronto

Copyright © 2012 ACM.

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Published: 19 May 2012

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May 19 - 22, 2012

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https://doi.org/10.1109/FOCS61266.2024.00027
Alman JBłasiok J(2023)Matrix Multiplication and Number on the Forehead CommunicationProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.16(1-23)Online publication date: 17-Jul-2023
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2023.16
Assadi S(2023)Recent Advances in Multi-Pass Graph Streaming Lower BoundsACM SIGACT News10.1145/3623800.362380854:3(48-75)Online publication date: 11-Sep-2023
https://dl.acm.org/doi/10.1145/3623800.3623808
Assadi SBehnezhad SKhanna SLi HSaha BServedio R(2023)On Regularity Lemma and Barriers in Streaming and Dynamic MatchingProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585110(131-144)Online publication date: 2-Jun-2023
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Assadi SSundaresan J(2023)Hidden Permutations to the Rescue: Multi-Pass Streaming Lower Bounds for Approximate Matchings2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00058(909-932)Online publication date: 6-Nov-2023
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Assadi SKol GOshman REmek YCachin C(2020)Lower Bounds for Distributed Sketching of Maximal Matchings and Maximal Independent SetsProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405732(79-88)Online publication date: 31-Jul-2020
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