Learn More
We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs(More)
A graph G has maximal local edge-connectivity k if the maximum number of edge-disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks-type theorems for k-connected graphs with maximal local edge-connectivity k, and for any graph with maximal local edge-connectivity 3. We also consider several related graph classes(More)
In two cases of paraplegia due to an inondation of the intrarachidian plexus by venous blood from the left venal vein, we studied the frequency with which the renal-rachidian trunk connected the left renal vein and the intrarachidian plexus. We show in these rare cases how it is possible, with a simple procedure, the ligature of the renal-rachidian trunk,(More)
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes of graphs that do not contain as a subgraph and as an induced subgraph, a cycle with a node that has at least two(More)
The urethral syndrome is a frequently encountered psychosomatic disorder; it constitutes the main complaint of some 20% of all women who consult a urologist. After a brief survey of the history of this syndrome, the authors examine 55 case reports of women with the urethral syndrome. The authors particularly emphasize the significance of the manner in which(More)
A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We prove that every graph that does not contain a wheel as a subgraph is 3-colorable. Résumé : Une roue est un graph formé d'un cycle(More)
In [Structural properties and decomposition of linear balanced matrices , Mathematical Programming, 55:129–168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear(More)