A note on color-bias Hamilton cycles in dense graphs

Andrea Freschi, Joseph Hyde, Joanna Lada, Andrew Treglown

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Balogh, Csaba, Jing, and Pluhár [Electron. J. Combin., 27 (2020)] recently determined the minimum degree threshold that ensures a 2-colored graph $G$ contains a Hamilton cycle of significant color bias (i.e., a Hamilton cycle that contains significantly more than half of its edges in one color). In this short note we extend this result, determining the corresponding threshold for $r$-colorings.
Original languageEnglish
Pages (from-to)970-975
JournalSIAM Journal on Discrete Mathematics
Issue number2
Publication statusPublished - 11 May 2021


  • Hamilton cycles
  • color-bias
  • discrepancy


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