Journal of Combinatorial Theory Series B
Discrete Mathematics
Powers of distance-hereditary graphs
Discrete Mathematics
European Journal of Combinatorics - Special issue on discrete metric spaces
Regular Article: Trees, Taxonomy, and Strongly Compatible Multi-state Characters
Advances in Applied Mathematics
Graph classes: a survey
Retractions of finite distance functions onto tree metrics
Discrete Applied Mathematics
Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
Packing and Covering δ-Hyperbolic Spaces by Balls
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Computing the hyperbolicity constant
Computers & Mathematics with Applications
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Given a connected graph G, we take, as usual, the distance xy between any two vertices x, y of G to be the length of some geodesic between x and y. The graph G is said to be δ-hyperbolic, for some δ ≥ 0, if for all vertices x, y, u, v in G the inequality xy + uv ≤ max{xu + yv, xv + yu} + δ holds, and G is bridged if it contains no finite isometric cycles of length four or more. In this paper, we will show that a finite connected bridged graph is 1-hyperbolic if and only if it does not contain any of a list of six graphs as an isometric subgraph.