We prove that sparse string graphs in a fixed surface have linear expansion. We extend this result to the more general setting of sparse region intersection graphs over any proper minor-closed class. The proofs are combinatorial and self-contained, and provide bounds that are within a constant factor of optimal. Applications of our results to graph colouring are presented.

翻译：我们证明，在固定曲面上的稀疏弦图具有线性扩张。我们将这一结论推广到任意真幺模闭类上的稀疏区域交图中。证明过程是组合且自包含的，并给出了常因子最优范围内的界。本文还展示了我们的结果在图着色中的应用。