Question

Find a recursive formula for the number of vertices nt in the graph Gt from the Kelly and Kelly proof of Proposition 5.25. Proposition 5.25. For every t > 3, there exists a graph G+ so that x(Gt) = t and w(Gt) = 2.

Answer 1

The recursive formula for the number of vertices in the graph Gt can be derived using the given equation n² = 2[n + 3 + .... + (2n - 3) + n].

Step-by-step explanation:

The recursive formula for the number of vertices nt in the graph Gt from the Kelly and Kelly proof of Proposition 5.25 can be derived using the given equation: n² = 2[n + 3 + .... + (2n - 3) + n].

To find the recursive formula, we can rewrite the equation as n² = 2[n + 3 + .... + (n + n)].

Next, we can simplify the expression by adding the terms inside the brackets and combining like terms, which gives us the recursive formula nt = 2(n + 3 + .... + n).