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One-legged caterpillars span hypercubes. (English) Zbl 0589.05031
A caterpillar is a tree with at least three vertices, which after removal of the end vertices and incident edges reduces to a snake or a simple vertex. A connected bipartite graph is called balanced if each part contains half of all vertices. It is shown that any balanced caterpillar having $$2^ n$$ vertices and maximum degree 3 spans the n-dimensional hypercube.
Reviewer: P.Kirschenhofer

##### MSC:
 05C05 Trees
##### Keywords:
caterpillar; hypercube
Full Text:
##### References:
 [1] Graph Theory. Addison-Wesley, Reading, MA (1969). [2] Harary, Discrete Math. 6 pp 359– (1973) [3] Havel, Čas. Pěst. Mat. 109 pp 135– (1984) [4] Nebeský, Čas. Pěst. Mat. 99 pp 164– (1974)
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