
A connected graph is bridged if it contains no isometric cycles of length more than 3, and it is 1-hyperbolic if for any 4 vertices the largest sum of diagonal distances is at most 1 higher than the second largest. It is shown that a graph satisfies both properties if and only if it does not contain any of 6 specified graphs as an isometric subgraph.
Distance in graphs, Computational Theory and Mathematics, thin graph, DISTANCE-HEREDITARY GRAPHS, hyperbolic graphs, Structural characterization of families of graphs, bridged graph, Geometry and Topology, Paths and cycles, Theoretical Computer Science
Distance in graphs, Computational Theory and Mathematics, thin graph, DISTANCE-HEREDITARY GRAPHS, hyperbolic graphs, Structural characterization of families of graphs, bridged graph, Geometry and Topology, Paths and cycles, Theoretical Computer Science
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