J. Graph Theory 35 (2000), no. 2, 89--98. MR1781190 (2001d:05162)
An {\em edge-labeling} $f$ of a graph $G$ is an injection from $E(G)$ to the set of integers. The {\em edge-bandwidth} of $G$ is $B'(G)=\min_f \{B'(f)\}$, where $B'(f)$ is the maximum difference between labels of incident edges of $G$. The {\em theta graph} $\Theta(l_1,\ldots,l_m)$ is the graph consisting of $m$ pairwise internally disjoint paths with common endpoints and lengths $l_1 \leq \cdots \leq l_m$.
We determine the edge bandwidth of all theta graphs.
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