Additive Spanners for k-Chordal Graphs
نویسندگان
چکیده
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 · logn) 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 · logn) 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
منابع مشابه
Collective Tree Spanners in Graphs with Bounded Genus, Chordality, Tree-Width, or Clique-Width
In this paper we study collective additive tree spanners for special families of graphs including planar graphs, graphs with bounded genus, graphs with bounded tree-width, graphs with bounded cliquewidth, and graphs with bounded chordality. We say that a graph G = (V,E) admits a system of μ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that...
متن کاملCollective Tree Spanners of Graphs
In this paper we introduce a new notion of collective tree spanners. We say that a graph G = (V,E) admits a system of μ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈ T (G) exists such that dT (x, y) ≤ dG(x, y) + r. Among other results, we show that any chordal graph, chordal bipartite ...
متن کاملSpanners for bounded tree-length graphs
This paper concerns construction of additive stretched spanners with few edges for n-vertex graphs having a tree-decomposition into bags of diameter at most δ, i.e., the tree-length δ graphs. For such graphs we construct additive 2δ-spanners with O(δn+n log n) edges, and additive 4δ-spanners with O(δn) edges. This provides new upper bounds for chordal graphs for which δ = 1. We also show a lowe...
متن کاملCollective Additive Tree Spanners of Homogeneously Orderable Graphs
In this paper we investigate the (collective) tree spanners problem in homogeneously orderable graphs. This class of graphs was introduced by A. Brandstädt et al. to generalize the dually chordal graphs and the distance-hereditary graphs and to show that the Steiner tree problem can still be solved in polynomial time on this more general class of graphs. In this paper, we demonstrate that every...
متن کاملAdditive 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 l...
متن کامل