Resonance graphs of catacondensed even ring systems are median
Discrete Mathematics
Quasi-median graphs, their generalizations, and tree-like equalities
European Journal of Combinatorics
Fast recognition algorithms for classes of partial cubes
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Recognizing partial cubes in quadratic time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the remoteness function in median graphs
Discrete Applied Mathematics
Fast recognition algorithms for classes of partial cubes
Discrete Applied Mathematics
A tight axiomatization of the median procedure on median graphs
Discrete Applied Mathematics
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Let M(m,n) be the complexity of checking whether a graph G with medges and n vertices is a median graph. We show that the complexity of checking whether Gis triangle-free is at most O(M(m,m)). Conversely, we prove that the complexity of checking whether a given graph is a median graph is at most O(m log n + T(m log n,n)), where T(m,n) is the complexity of finding all triangles of the graph. We also demonstrate that, intuitively speaking, there are as many median graphs as there are triangle-free graphs. Finally, these results enable us to prove that the complexity of recognizing planar median graphs is linear.