Is it possible to split (each vertex should be exactly in one subgraph) a connected graph with 2n vertices into two induced subgraphs (each subgraph must have at least one vertex) so that the degree of each vertex of each subgraph becomes even?

Hello everyone! I was thinking about a new feature in CF and i think it's good to share it with you, the feature I'm thinking about is something called the beauty of the questions, meaning that people who solve a question can rate the beauty of the question. and thus each question has a score for its own beauty, which is specified by the people who solved the question. I think it will be better if I can sort the questions according to beauty and solve them. I'd love to hear what you think about this :)