Davoodi–Javadi–Kamranian–Raeisi multicolor star-forest conjecture

Let $t$ be an integer, let $a_{1},a_{2},\dots,a_{t}$ be positive integers, and set

$$a=\sum_{s=1}^{t}a_{s}.$$

For each $s\in[t]$, let $n_{1}^{s}\geq n_{2}^{s}\geq\cdots\geq n_{a_{s}}^{s}\geq1$ be integers. For each $k\in[a]\backslash[t-1]$, define

$$\ell_{k}=\max\left\{\sum_{s=1}^{t}n_{i_{s}}^{s}-t+1:\sum_{s=1}^{t}i_{s}=k\right\}.$$

Davoodi–Javadi–Kamranian–Raeisi conjecture. The multicolor size Ramsey number satisfies

$$\hat{r}\left(\bigsqcup_{i=1}^{a_{1}}K_{1,n_{i}^{1}},\bigsqcup_{i=1}^{a_{2}}K_{1,n_{i}^{2}},\dots,\bigsqcup_{i=1}^{a_{t}}K_{1,n_{i}^{t}}\right)=\sum_{k=t}^{a}\ell_{k}.$$

This extends the two-color star-forest conjecture to multiple colors and is presented as a conjectural generalization; no resolution is given in the supplied text.