Balanced Caterpillars of Maximum Degree 3 and with Hairs of Arbitrary Length Are Subgraphs of Their Optimal Hypercube

A caterpillar C is a tree having a path that contains all vertices of C of degree at least 3. We show in this article that every balanced caterpillar with maximum degree 3 and 2(n) vertices is a subgraph of the n-dimensional hypercube. This solves a long-standing open problem and generalizes a result of Havel and Liebl (1986), who considered only such caterpillars that have a path containing all vertices of degree at least 2.