Laurent Beaudou

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8 Abstract A special case of a combinatorial theorem of De Bruijn and Erd˝ os asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by(More)
One of the De Bruijn-Erd˝ os theorems deals with finite hypergraphs where every two vertices belong to precisely one hyperedge. It asserts that, except in the perverse case where a single hyperedge equals the whole vertex set, the number of hyperedges is at least the number of vertices and the two numbers are equal if and only if the hypergraph belongs to(More)
It is already known that for very small edge cuts in graphs, the crossing number of the graph is at least the sum of the crossing number of (slightly augmented) components resulting from the cut. Under stronger connectivity condition in each cut component that was formalized as a graph operation called zip product, a similar result was obtained for edge(More)
Given a directed graph D = (V, A) we define its intersection graph I(D) = (A, E) to be the graph having A as a node-set and two nodes of I(D) are adjacent if their corresponding arcs share a common node that is the tail of at least one of these arcs. We call these graphs facility location graphs since they arise from the classical uncapacitated facility(More)
We present a necessary and sufficient condition for a graph of odd-girth 2k + 1 to bound the class of K 4-minor-free graphs of odd-girth (at least) 2k + 1, that is, to admit a homomorphism from any such K 4-minor-free graph. This yields a polynomial-time algorithm to recognize such bounds. Using this condition, we first prove that every K 4-minor free graph(More)