Drawing disconnected graphs on the Klein bottle

We prove that two disjoint graphs must always be drawn separately on the Klein bottle, in order to minimize the crossing number of the whole drawing.Comment: 13 pages, second version, major changes in the proo

A História da Alimentação: balizas historiográficas

Os M. pretenderam traçar um quadro da História da Alimentação, não como um novo ramo epistemológico da disciplina, mas como um campo em desenvolvimento de práticas e atividades especializadas, incluindo pesquisa, formação, publicações, associações, encontros acadêmicos, etc. Um breve relato das condições em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biológica, a econômica, a social, a cultural e a filosófica!, assim como da identificação das contribuições mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histórica, foi ela organizada segundo critérios morfológicos. A seguir, alguns tópicos importantes mereceram tratamento à parte: a fome, o alimento e o domínio religioso, as descobertas européias e a difusão mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rápido balanço crítico da historiografia brasileira sobre o tema

The st-bond polytope on series-parallel graphs

International audienceThe st-bond polytope of a graph is the convex hull of the incidence vectors of its st-bonds, where an st-bond is a minimal st-cut. In this paper, we provide a linear description of the st-bond polytope on series-parallel graphs. We also show that the st-bond polytope is the intersection of the st-cut dominant and the bond polytope

Covering symmetric semi-monotone functions

AbstractWe define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0,1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augmentation problem. Our contribution is to provide a significantly simpler and shorter proof

Augmentation de l'arête-connexité

Un graphe est k-arête-connexe si lui retirer moins de k arêtes ne le déconnecte pas. L'augmentation de l'arête-connexité d'un graphe consiste à, étant donné un entier k et un graphe, ajouter un nombre minimal d'arêtes au graphe afin de la rendre k-arête-connexe. Depuis la résolution de ce problème, de nombreuses variantes ont été etudiées : par exemple l'augmentation de l'arête-connexité d'un graphe sous contraintes de partition ; l'augmentation de l'arête-connexité d'un hypergraphe ; ou encore les problèmes de recouvrement de fonctions, généralisations abstraites des problèmes d'augmentation. Le but de cette thèse est d'unifier différents résultats du domaine. Nous y résolvons d'abord l'augmentation de l'arête-connexité d'un hypergraphe sous contraintes de partition, puis sa généralisation abstraite, le recouvrement d'une fonction symétrique surmodulaire croisée sous contraintes de partition. Finalement, nous résolvons le recouvrement d'une fonction symétrique semi-monotone.A graph is k-edge-connected if removing less than k edges does not disconnect it. The problem of edge-connectivity augmentation of a graph is as follows : given a graph and a integer k, add a minimum number of edges to make the graph k-edge-connected. Since the problem was solved, many variants have been studied : for example edge-connectivity augmentation of a graph with partition constraints : edge-connectivity augmentation of a hypergraph : or problems of covering a function by a graph, abstract generalizations of the augmentation problems. The aim of this thesis is to unify various results of the field. First we solve the problem of edge-connectivity augmentation of a hypergraph with partition contraints, and then its abstract form, the partition constrainedcovering af a symmetric crossing supermodular function. Finally, we solve the covering of a symmetric semi-monotone function.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Augmenting the edge-connectivity of a hypergraph by adding a multipartite graph

International audienc

Partition constrained covering of symmetric crossing supermodular functions

International audienc

Augmenting the Edge-Connectivity of a Hypergraph by Adding a Multipartite Graph

International audienc

Trader multiflow and box-TDI systems in series-parallel graphs

Series–parallel graphs are known to be precisely the graphs for which the standard linear systems describing the cut cone, the cycle cone, the T-join polytope, the cut polytope, the multicut polytope and the T-join dominant are TDI. We prove that these systems are actually box-TDI. As a byproduct, our result yields a min–max relation for a new problem: the trader multiflow problem. The latter generalizes both the maximum multiflow and min-cost multiflow problems and we show that it is polynomial-time solvable in series–parallel graphs