We show that the existence of a homomorphism from an $n$-vertex graph $G$ to an $h$-vertex graph $H$ can be decided in time $2^{O(n)}h^{O(1)}$ and polynomial space if $H$ comes from a family of graphs that excludes a topological minor. The algorithm is based on a reduction to a single-exponential number of constraint satisfaction problems over tractable languages and can handle cost minimization. We also present an improved randomized algorithm for the special case where the graph $H$ is an odd cycle.

翻译：我们证明，若$H$来自一个排除拓扑子图的图族，则从$n$顶点图$G$到$h$顶点图$H$的同态存在性可在$2^{O(n)}h^{O(1)}$时间与多项式空间内判定。该算法基于将问题归约至可解语言上的单指数数量约束满足问题，并能处理代价最小化情形。针对目标图$H$为奇数环的特殊情况，我们还提出了一种改进的随机算法。