Additive Spanners for k-Chordal Graphs

Abstract. 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 Sch¨affer 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. Classification: Algorithms, Sparse Graph Spanners

• Type: Conference
• Year: 2003
• Where: CIAC
• Authors: Victor Chepoi, Feodor F. Dragan, Chenyu Yan
• Keywords: Additive 3-spanner, Additive 4-spanner, Algorithms, CIAC 2003, Graph Spanners