Large components in r ‐edge‐colorings of K n have diameter at most five

Reflecting on problems posed by Gyárfás [Ramsey Theory Yesterday, Today and Tomorrow, Birkhäuser, Basel, 2010, pp. 77–96] and Mubayi [Electron J Combin 9 (2002), #R42], we show in this note that every r ‐edge‐coloring of K n contains a monochromatic component of diameter at most five on at least n /( r −1) vertices. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:337–340, 2012