Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
Treewidth for graphs with small chordality
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Routing in Networks with Low Doubling Dimension
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
On Parameterized Path and Chordless Path Problems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Compact name-independent routing with minimum stretch
ACM Transactions on Algorithms (TALG)
Algorithms for finding an induced cycle in planar graphs and bounded genus graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Greedy forwarding in scale-free networks embedded in hyperbolic metric spaces
ACM SIGMETRICS Performance Evaluation Review
Treewidth and Hyperbolicity of the Internet
NCA '11 Proceedings of the 2011 IEEE 10th International Symposium on Network Computing and Applications
Distributed computing of efficient routing schemes in generalized chordal graphs
Theoretical Computer Science
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Cops and robber games concern a team of cops that must capture a robber moving in a graph. We consider the class of k-chordal graphs, i.e., graphs with no induced cycle of length greater than k, k≥3. We prove that k−1 cops are always sufficient to capture a robber in k-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including k-chordal graphs. We present a quadratic algorithm that, given a graph G and k≥3, either returns an induced cycle larger than k in G, or computes a tree-decomposition of G, each bag of which contains a dominating path with at most k−1 vertices. This allows us to prove that any k-chordal graph with maximum degree Δ has treewidth at most (k−1)(Δ−1)+2, improving the O(Δ(Δ−1)k−3) bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has small hyperbolicity. As an application, for any n-node graph admitting such a tree-decomposition, we propose a compact routing scheme using routing tables, addresses and headers of size O(logn) bits and achieving an additive stretch of O(klogΔ). As far as we know, this is the first routing scheme with O(k logΔ+logn)-routing tables and small additive stretch for k-chordal graphs.