Oriented discrepancy of Hamilton cycles

Lior Gishboliner, Michael Krivelevich, Peleg Michaeli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We propose the following extension of Dirac's theorem: if (Formula presented.) is a graph with (Formula presented.) vertices and minimum degree (Formula presented.), then in every orientation of (Formula presented.) there is a Hamilton cycle with at least (Formula presented.) edges oriented in the same direction. We prove an approximate version of this conjecture, showing that minimum degree (Formula presented.) guarantees a Hamilton cycle with at least (Formula presented.) edges oriented in the same direction. We also study the analogous problem for random graphs, showing that if the edge probability (Formula presented.) is above the Hamiltonicity threshold, then, with high probability, in every orientation of (Formula presented.) there is a Hamilton cycle with (Formula presented.) edges oriented in the same direction.

Original languageEnglish
Pages (from-to)780-792
Number of pages13
JournalJournal of Graph Theory
Volume103
Issue number4
DOIs
StatePublished - Aug 2023

Funding

FundersFunder number
USA–Israel BSF2018267
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung200021_196965

    Keywords

    • Dirac's theorem
    • Hamilton cycle
    • oriented discrepancy

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