Question: (5) Letr,b,9 > 2 be integers. Recall Rr, b, g) is the least integer n such that every 3-edge-coloured complete graph on at least n

(5) Letr,b,9 > 2 be integers. Recall Rr, b, g) is the least integer n such that every 3-edge-coloured complete graph on at least n vertices contains a red Kr, a blue Ky or a green K, (a) (3 marks) Show R(3,3,3) R(3,6). (Hint: Consider a 3-edge coloured complete graph K on at least n = R(3,6) vertices. If K, has no red K3. what structure can be found if we consider the blue and the green edges to be the same colour?) (b) (1 mark) Show Rr,b,g) RrR(b,g)). (5) Letr,b,9 > 2 be integers. Recall Rr, b, g) is the least integer n such that every 3-edge-coloured complete graph on at least n vertices contains a red Kr, a blue Ky or a green K, (a) (3 marks) Show R(3,3,3) R(3,6). (Hint: Consider a 3-edge coloured complete graph K on at least n = R(3,6) vertices. If K, has no red K3. what structure can be found if we consider the blue and the green edges to be the same colour?) (b) (1 mark) Show Rr,b,g) RrR(b,g))

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