This paper presents a linear time algorithm for determining whether the treewidth of a graph is at most a constant k, and if so, finding a tree-decomposition of the graph with treewidth at most k. The algorithm is based on partitioning the graph's vertices into low-degree and high-degree sets, and using a recursive approach to reduce the problem to smaller subproblems. The algorithm efficiently handles both cases where there are many low-degree vertices and where there are few, by either finding a maximal matching or adding edges to the graph to identify I-simplicial vertices. The algorithm ensures that the resulting tree-decomposition has treewidth at most k, and it uses linear time and memory. The result has important implications for the recognition of minor-closed graph classes that do not contain all planar graphs, as it implies that such classes can be recognized in linear time. The algorithm is efficient and has a linear time complexity, making it suitable for practical applications.This paper presents a linear time algorithm for determining whether the treewidth of a graph is at most a constant k, and if so, finding a tree-decomposition of the graph with treewidth at most k. The algorithm is based on partitioning the graph's vertices into low-degree and high-degree sets, and using a recursive approach to reduce the problem to smaller subproblems. The algorithm efficiently handles both cases where there are many low-degree vertices and where there are few, by either finding a maximal matching or adding edges to the graph to identify I-simplicial vertices. The algorithm ensures that the resulting tree-decomposition has treewidth at most k, and it uses linear time and memory. The result has important implications for the recognition of minor-closed graph classes that do not contain all planar graphs, as it implies that such classes can be recognized in linear time. The algorithm is efficient and has a linear time complexity, making it suitable for practical applications.