Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering. A knowledge base is then composed of an instance that contains incomplete data and a set of existential rules, and answers to queries are logically entailed from the knowledge base. This brought again to light the fundamental chase tool, and its different variants that have been proposed in the literature. It is well-known that the problem of determining, given a chase variant and a set of existential rules, whether the chase will halt on a given instance / on any instance, is undecidable. Hence, a crucial issue is whether it becomes decidable for known subclasses of existential rules. We consider linear existential rules, a simple yet important subclass of existential rules. We study the decidability of the associated chase termination problem for different chase variants, with a novel approach based on a single graph and a single notion of forbidden pattern. Besides the theoretical interest of a unified approach, an original result is the decidability of the restricted chase termination for linear existential rules.