Textual entailment is a fundamental task in natural language processing. Most approaches for solving this problem use only the textual content present in training data. A few approaches have shown that information from external knowledge sources like knowledge graphs (KGs) can add value, in addition to the textual content, by providing background knowledge that may be critical for a task. However, the proposed models do not fully exploit the information in the usually large and noisy KGs, and it is not clear how it can be effectively encoded to be useful for entailment. We present an approach that complements text-based entailment models with information from KGs by (1) using Personalized PageRank to generate contextual subgraphs with reduced noise and (2) encoding these subgraphs using graph convolutional networks to capture the structural and semantic information in KGs. We evaluate our approach on multiple textual entailment datasets and show that the use of external knowledge helps the model to be robust and improves prediction accuracy. This is particularly evident in the challenging BreakingNLI dataset, where we see an absolute improvement of 5-20% over multiple text-based entailment models.