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Thanks to the capacity for long-range dependencies and robustness to irregular shapes, vision transformers and deformable convolutions are emerging as powerful vision techniques of segmentation.Meanwhile, Graph Convolution Networks (GCN) optimize local features based on global topological relationship modeling. Particularly, they have been proved to be effective in addressing issues in medical imaging segmentation tasks including multi-domain generalization for low-quality images. In this paper, we present a novel, effective, and robust framework for medical image segmentation, namely, UGformer. It unifies novel transformer blocks, GCN bridges, and convolution decoders originating from U-Net to predict left atriums (LAs) and LA scars. We have identified two appealing findings of the proposed UGformer: 1). an enhanced transformer module with deformable convolutions to improve the blending of the transformer information with convolutional information and help predict irregular LAs and scar shapes. 2). Using a bridge incorporating GCN to further overcome the difficulty of capturing condition inconsistency across different Magnetic Resonance Images scanners with various inconsistent domain information. The proposed UGformer model exhibits outstanding ability to segment the left atrium and scar on the LAScarQS 2022 dataset, outperforming several recent state-of-the-arts.