Abstract: In this short note we study two questions about the existence of subgraphs of the hypercube $Q_n$ with certain properties. The first question, due to Erdős–Hamburger–Pippert–Weakley, asks whether there exists a bounded degree subgraph of $Q_n$ which has diameter $n$. We answer this question by giving an explicit construction of such a subgraph with maximum degree at most 120.
The second problem concerns properties of $k$-additive spanners of the hypercube, that is, subgraphs of $Q_n$ in which t… Show more
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