期刊
JOURNAL OF GRAPH THEORY
卷 99, 期 2, 页码 247-250出版社
WILEY
DOI: 10.1002/jgt.22739
关键词
diameter; monochromatic component; Ramsey theory
类别
资金
- J. William Fulbright Educational Exchange Program
- Simons Foundation
- Nemzeti Kutatasi Fejlesztesi es Innovacios Hivatal
In a 3-edge-coloring of Kn, there either exists a monochromatic component with a diameter of at most three spanning at least n / 2 vertices, or every color class is spanning and has a diameter of at most four.
Gyarfas conjectured in 2011 that every r-edge-colored K n contains a monochromatic component of bounded (perhaps three) diameter on at least n / ( r - 1 ) vertices. Letzter proved this conjecture with diameter four. In this note we improve the result in the case of r = 3: We show that in every 3-edge-coloring of K n either there is a monochromatic component of diameter at most three on at least n / 2 vertices or every color class is spanning and has diameter at most four.
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