Abstract: Albeit existing Single-Domain Generalized Object Detection (Single-DGOD) methods enable models to generalize to unseen domains, most assume that the training and testing data share the same label space. In real-world scenarios, unseen domains often introduce previously unknown objects, a challenge that has been largely overlooked. In this paper, we tackle the practical problem of Single-domain Generalizable Open-Set Object Detection (SG-OSOD), which addresses both unseen domains and unknown classes. We identify two key challenges: (1) detecting unknown classes with only known-class data, and (2) learning robust features to mitigate domain shift. To address these challenges, we propose the framework termed $\texttt{ASGS}$, which leverages adaptive subgraph structures to enhance the understanding of unknown scenes and classes. $\texttt{ASGS}$ consists of Subgraph-wise Unknown-class Learning (SUL) and Class-wise Embedding Compaction (CEC). SUL employs non-parametric methods to detect unknown samples and performs Adaptive Subgraph Searching (ASS) for high-order structural feature extraction, enabling domain-robust unknown class learning. Moreover, the CEC module enhances class discrimination robustness through contrastive learning, which results in more compact class clusters in unknown scenarios. Experimental results demonstrate the effectiveness of the proposed $\texttt{ASGS}$.