Bipartitions of Highly Connected Tournaments

Jaehoon Kim; Daniela Kuhn; Deryk Osthus

doi:10.1137/15M1006611

Bipartitions of Highly Connected Tournaments

Jaehoon Kim, Daniela Kuhn, Deryk Osthus

Mathematics

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4 Citations (Scopus)

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Abstract

We show that if T is a strongly 10⁹k⁶ log(2k)-connected tournament, there exists
a partition A;B of V (T) such that each of T[A], T[B] and T[A;B] is strongly k-connected.
This provides solutions to tournament analogues of two partition conjectures of Thomassen regarding highly connected graphs. We also discuss spanning linkages as well as non-separating subdivisions in highly connected tournaments.

Original language	English
Pages (from-to)	895–911
Journal	SIAM Journal on Discrete Mathematics
Volume	30
Issue number	2
Early online date	12 May 2016
DOIs	https://doi.org/10.1137/15M1006611
Publication status	E-pub ahead of print - 12 May 2016

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abstract = "We show that if T is a strongly 109k6 log(2k)-connected tournament, there existsa partition A;B of V (T) such that each of T[A], T[B] and T[A;B] is strongly k-connected.This provides solutions to tournament analogues of two partition conjectures of Thomassen regarding highly connected graphs. We also discuss spanning linkages as well as non-separating subdivisions in highly connected tournaments.",

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AB - We show that if T is a strongly 109k6 log(2k)-connected tournament, there existsa partition A;B of V (T) such that each of T[A], T[B] and T[A;B] is strongly k-connected.This provides solutions to tournament analogues of two partition conjectures of Thomassen regarding highly connected graphs. We also discuss spanning linkages as well as non-separating subdivisions in highly connected tournaments.

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JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

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Bipartitions of Highly Connected Tournaments

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