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Improved Upper Bounds for Gallai–Ramsey Numbers of Paths and Cycles
Author(s) -
Hall Martin,
Magnant Colton,
Ozeki Kenta,
Tsugaki Masao
Publication year - 2014
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.21723
Subject(s) - combinatorics , mathematics , ramsey's theorem , monochromatic color , upper and lower bounds , graph , integer (computer science) , rainbow , discrete mathematics , complete graph , computer science , mathematical analysis , botany , physics , quantum mechanics , biology , programming language
Given a graph G and a positive integer k , define the Gallai–Ramsey number to be the minimum number of vertices n such that any k ‐edge coloring of K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G . In this work, we improve upon known upper bounds on the Gallai–Ramsey numbers for paths and cycles. All these upper bounds now have the best possible order of magnitude as functions of k .