Halin

Halin is a surname of German origin. In mathematics, Halin is best known as the name of a class of graphs named after the German mathematician Rudolf Halin, who introduced them in graph theory.

The Halin construction starts from a finite tree with no vertices of degree two and adds a cycle through all leaves in their order around the tree. The resulting graph is planar, and each leaf becomes incident to two cycle edges plus its edge to the tree, giving leaves degree three.

Halin graphs are planar and contain a Hamiltonian cycle. They are studied as natural examples that connect tree topology with planar augmentation and are used in discussions of graph algorithms, planarity, and network design.

Beyond mathematics, Halin appears as a surname in various countries, and individuals bearing the name have contributed to science and culture. In scholarly contexts, Halin most commonly refers to Rudolf Halin and to Halin graphs.