Given that, whenever every edge of the complete graph K_2k is coloured red or blue, there exists a monochromatic copy of S_k as a subgraph of the coloured K_2k .

2. Let k be a positive integer. A star S, is a tree on k + 1 vertices with one of the vertices having degree k and the other k vertices each having degree 1. () Find all values of k such that the edges of the complete graph K2-2 can be coloured red or blue without containing a monochromatic copy of S: as a subgraph of the coloured K24-1. Justify your answer. 2. Let k be a positive integer. A star S, is a tree on k + 1 vertices with one of the vertices having degree k and the other k vertices each having degree 1. () Find all values of k such that the edges of the complete graph K2-2 can be coloured red or blue without containing a monochromatic copy of S: as a subgraph of the coloured K24-1. Justify your