Menu
A \(k\)-labeling of a graph is a labeling of the vertices of the graph by \(k\)-tuples of non-negative integers such that two vertices of \(G\) are adjacent if and only if their label \(k\)-tuples differ in each coordinate. The dimension of a graph \(G\) is the least \(k\) such that \(G\) has a \(k\)-labeling.
Lovász et al. showed that for \(n \geq 3\), the dimension of a path of length \(n\) is \((\log_2 n)^+\). Lovász et al. and Evans et al. determined the dimension of a cycle of length \(n\) for most values of \(n\). In the present paper, we obtain the dimension of a caterpillar or provide close bounds for it in various cases.