TY - JOUR

T1 - Oriented discrepancy of Hamilton cycles

AU - Gishboliner, Lior

AU - Krivelevich, Michael

AU - Michaeli, Peleg

N1 - Publisher Copyright:
© 2023 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.

PY - 2023/8

Y1 - 2023/8

N2 - 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.

AB - 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.

KW - Dirac's theorem

KW - Hamilton cycle

KW - oriented discrepancy

UR - http://www.scopus.com/inward/record.url?scp=85149339867&partnerID=8YFLogxK

U2 - 10.1002/jgt.22947

DO - 10.1002/jgt.22947

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AN - SCOPUS:85149339867

SN - 0364-9024

VL - 103

SP - 780

EP - 792

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 4

ER -