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Among different existing graph self-supervised learning strategies, graph contrastive learning (GCL) has been one of the most prevalent approaches to this problem. Despite the remarkable performance those GCL methods have achieved, existing GCL methods that heavily depend on various manually designed augmentation techniques still struggle to alleviate the feature suppression issue without risking losing task-relevant information. Consequently, the learned representation is either brittle or unilluminating. In light of this, we introduce the Graph Contrastive Learning with Cross-View Reconstruction (GraphCV), which follows the information bottleneck principle to learn minimal yet sufficient representation from graph data. Specifically, GraphCV aims to elicit the predictive (useful for downstream instance discrimination) and other non-predictive features separately. Except for the conventional contrastive loss which guarantees the consistency and sufficiency of the representation across different augmentation views, we introduce a cross-view reconstruction mechanism to pursue the disentanglement of the two learned representations. Besides, an adversarial view perturbed from the original view is added as the third view for the contrastive loss to guarantee the intactness of the global semantics and improve the representation robustness. We empirically demonstrate that our proposed model outperforms the state-of-the-art on graph classification task over multiple benchmark datasets.