For two graphs $H_1$ and H2, the Ramsey number $r(H_1, H_2)$ is the minimum number r so that in any red-blue coloring of the edges of the complete graph Kr on r vertices there is necessarily either a red copy of $H_1$ or a blue copy of $H_2$ (or both).
Let $\def\star#1{K_{1,#1}}\star n$ denote the star with $n$ edges. Compute the Ramsey number $r(\star n, \star m)$ for all values of $m$ and $n$.
My approach was to look at a vertex in $K_r$ and observe when its degree is big enough for there to be enough edges such that one of the stars has to appear. My problem is that I do not understand how to show it's the minimal number (or even if it is true).
My second issue is that I was given a hint that the formula depends on the parity of $n$ and $m$, and my approach does not address this, which suggests it may be flawed.
Would appreciate some guidnace.
Thanks.