University students learn to write proofs in a variety of contexts, including specific content courses and transition-to-proof courses. In this chapter, we consider domain-specific aspects of proof, exemplified via case study. By domain-specific aspects of proof, we mean those proof techniques that occur characteristically within a given domain, often as manifestations of common proof techniques that occur across domains. The “new direction” for research on proof that we are promoting, then, is to identity and study such proof techniques and such manifestations that are domain-specific in this way. We focus here on proof within combinatorics and graph theory, offering both an exhortation to explore domain-specific aspects of proof, and a model of what such initial exploration could entail. We present three contributions. First, we highlight domain-specific manifestations of common proof techniques (specifically, proof by contradiction, induction, and extremality). Second, we argue that proofs in graph theory and combinatorics often necessitate specifying and formalizing on the part of the prover. Third, we discuss ways in which graph theory and combinatorics are well-suited for explorations related to algorithmic proofs. For each of these contributions, we discuss potential future research avenues for proof education researchers.