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Following problems posed by Gy\'arf\'as, we show that for every$r$-edge-colouring of $K_n$ there is a monochromatic triple star of order atleast $n/(r-1)$, improving a previous result by Ruszink\'o.  An edge colouring of a graph is called a local $r$-colouring if every vertexspans edges of at most $r$ distinct colours. We prove the existence of amonochromatic triple star with at least $rn/(r^2-r+1)$ vertices in every local$r$-colouring of $K_n$.

Large monochromatic triple stars in edge colourings