Collaborative perception in unknown environments is crucial for multi-robot systems. With the emergence of foundation models, robots can now not only perceive geometric information but also achieve open-vocabulary scene understanding. However, existing map representations that support open-vocabulary queries often involve large data volumes, which becomes a bottleneck for multi-robot transmission in communication-limited environments. To address this challenge, we develop a method to construct a graph-structured 3D representation called COGraph, where nodes represent objects with semantic features and edges capture their spatial adjacency relationships. Before transmission, a data-driven feature encoder is applied to compress the feature dimensions of the COGraph. Upon receiving COGraphs from other robots, the semantic features of each node are recovered using a decoder. We also propose a feature-based approach for place recognition and translation estimation, enabling the merging of local COGraphs into a unified global map. We validate our framework on two realistic datasets and the real-world environment. The results demonstrate that, compared to existing baselines for open-vocabulary map construction, our framework reduces the data volume by over 80\% while maintaining mapping and query performance without compromise. For more details, please visit our website at https://github.com/efc-robot/MR-COGraphs.