Large Monochromatic Triple Stars in Edge Colourings

Following problems posed by Gyárfás 2011, we show that for every r‐edge‐colouring of there is a monochromatic triple star of order at least , improving Ruszinkó's result 2012. An edge colouring of a graph is called a local r‐colouring if every vertex spans edges of at most r distinct colours. We prove the existence of a monochromatic triple star with at least vertices in every local r‐colouring of .