Additive sparse spanners for graphs with bounded length of largest induced cycle

In this paper, we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n− 2 edges and an additive 3-spanner with at most O(n log n) edges. This significantly improves results of Peleg and Schäffer from [Graph Spanners, J. Graph Theory 13 (1989) 99–116]. Our spanners are additive and easier to construct.An additive 4-spanner can be constructed in linear time while an additive 3-spanner is constructable in O(m log n) time. Furthermore, our method can be extended to graphs with largest induced cycles of length k. Any such graph admits an additive (k + 1)-spanner with at most 2n− 2 edges which is constructable in O(n k +m) time. © 2005 Elsevier B.V. All rights reserved.