Gallai–Ramsey number for K5 ${K}_{5}$

Magnant, Colton; Schiermeyer, Ingo

doi:10.1002/jgt.22835

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2022

2024

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Cited by 8 publications

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“…In [5], Gyárfás, Sárközy, Sebő, Selkow used this connection to show that 2coloured Ramsey-type results for certain families of graphs, which are called Gallai-extendable, can be extended to Gallai colourings. More Ramsey-type problems for Gallai colourings are investigated in [5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Realising every colour distribution sequence with a Gallai colouring

Yan¹

2023

Preprint

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An edge colouring of Kn with k colours is a Gallai k-colouring if it does not contain any rainbow triangle. Gyárfás, Pálvölgyi, Patkós and Wales proved that there exists a number g(k) such that n ≥ g(k) if and only if for any colour distribution sequence (e1,, there exist a Gallai k-colouring of Kn with ei edges having colour i. They also showed that Ω(k) = g(k) = O(k 2 ) and posed the problem of determining the exact order of magnitude of g(k). Feffer, Fu and Yan improved both bounds significantly by proving Ω(k .5 ). We resolve this problem by showing g(k) = Θ(k 1.5 /(log k) 0.5 ).

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