Resonance graphs of catacondensed even ring systems are median
Discrete Mathematics
Interval routing in some planar networks
Theoretical Computer Science
Fiber-complemented graphs II. Retractions and endomorphisms
Discrete Mathematics
Median problem in some plane triangulations and quadrangulations
Computational Geometry: Theory and Applications
The algebra of metric betweenness I: Subdirect representation and retraction
European Journal of Combinatorics
Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
Tight spans of distances and the dual fractionality of undirected multiflow problems
Journal of Combinatorial Theory Series B
A self-stabilizing algorithm for the median problem in partial rectangular grids and their relatives
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
The maximum multiflow problems with bounded fractionality
Proceedings of the forty-second ACM symposium on Theory of computing
Combinatorics and Geometry of Finite and Infinite Squaregraphs
SIAM Journal on Discrete Mathematics
Cop and Robber Games When the Robber Can Hide and Ride
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Theory Series B
Shortest path problem in rectangular complexes of global nonpositive curvature
Computational Geometry: Theory and Applications
On embeddings of CAT(0) cube complexes into products of trees via colouring their hyperplanes
Journal of Combinatorial Theory Series B
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In this note, we characterize the graphs (1-skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov's CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if, in addition, all maximal cells are either regular Euclidean cubes or right Euclidean triangles glued in a special way, then the underlying graph G(K) is either a median graph or a hereditary modular graph without two forbidden induced subgraphs. We also characterize the simplicial complexes arising from bridged graphs, a class of graphs whose metric enjoys one of the basic properties of CAT(0) spaces. Additionally, we show that the graphs of all these complexes and some more general classes of graphs have geodesic combings and bicombings verifying the 1- or 2-fellow traveler property.