Gallai‐Ramsey number for    K  4 | Zendy

Liu Henry | Zendy; Magnant Colton | Zendy; Saito Akira | Zendy; Schiermeyer Ingo | Zendy; Shi Yongtang | Zendy

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Gallai‐Ramsey number for K 4

Author(s) -

Liu Henry,

Magnant Colton,

Saito Akira,

Schiermeyer Ingo,

Shi Yongtang

Publication year - 2020

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22514

Subject(s) - combinatorics , mathematics , ramsey's theorem , conjecture , monochromatic color , rainbow , graph , integer (computer science) , discrete mathematics , computer science , physics , quantum mechanics , programming language , botany , biology

Given a graph H , the k ‐colored Gallai‐Ramsey number g r k ( K 3 ⁢ : H )is defined to be the minimum integer n such that every k ‐coloring (using all k colors) of the complete graph on n vertices contains either a rainbow triangle or a monochromatic copy of H . Recently, Fox et al [J. Combin. Theory Ser. B, 111 (2015), pp. 75–125] conjectured the value of the Gallai‐Ramsey numbers for complete graphs. We verify this conjecture for the first open case, where H = K 4 .

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