We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make use of information about the colours assigned so far to determine our future choices. The interactive sum choice number cannot exceed the sum choice number and we conjecture that, except in the case of complete graphs, the interactive sum choice number is always strictly smaller than the sum choice number. In this paper we provide evidence in support of this conjecture, demonstrating that it holds for a number of graph classes, and indeed that in many cases the difference between the two quantities grows as a linear function of the number of vertices.

翻译：我们引入了一个经过仔细研究的图表和选择数的变量, 我们称之为交互式和选择数。 在这个变量中, 我们请求将颜色一次添加到脊椎的颜色列表中, 这样我们就能够利用迄今为止所分配的颜色信息来决定我们的未来选择。 交互式和选择数不能超过总选择数, 我们推测, 除了完整的图表, 交互式和选择数总是绝对小于总选择数。 在本文中, 我们提供了支持这一推测的证据, 证明它持有一些图表类别, 并且实际上在许多情况下, 两个数量之间的差异会随着脊椎数的线性函数而增长 。