Résumé: The MAELIA project consists in modeling the socio-environmental impacts of norms designing the management and governance of renewable natural resources and of the environment. In this paper we present the MAELIA project and in particular its network-like structures: several sub-systems of different nature (environmental, social, normative sub-systems) emerge and interact in a complex manner. This network point of view on the MAELIA platform will allow to use and to develop tools relying on graph theory and network analysis in order to understand the structures of these different interacting complex systems, to construct a platform taking into consideration these interactions and to build various scenarios for the analysis of the social and environmental coupled system sustainability.

Ref HAL: inria-00628061_v1

Ref HAL: hal-00716574_v1
DOI: 10.1016/j.ejc.2008.02.012
Résumé: We introduce the Convex Circuit-Free coloration and Convex Circuit-Free chromatic numberView the MathML source of an oriented graph View the MathML source and establish various basic results. We show that the problem of deciding if an oriented graph verifies View the MathML source is NP-complete if k≥3, and polynomial if k≤2. We introduce an algorithm which finds the optimal convex circuit-free coloration for tournaments, and characterize the tournaments that are vertex-critical for the convex circuit-free coloration.

Ref Arxiv: 0809.1751
Résumé: A flag complex can be defined as a simplicial complex whose simplices correspond to complete subgraphs of its 1-skeleton taken as a graph. In this article, by introducing the notion of s-dismantlability, we shall define the s-homotopy type of a graph and show in particular that two finite graphs have the same s-homotopy type if, and only if, the two flag complexes determined by these graphs have the same simplicial simple-homotopy type (Theorem 2.10, part 1). This result is closely related to similar results established by Barmak and Minian (Adv. in Math., 218 (2008), 87-104) in the framework of posets and we give the relation between the two approaches (theorems 3.5 and 3.7). We conclude with a question about the relation between the s-homotopy and the graph homotopy defined by Chen, Yau and Yeh (Discrete Math., 241(2001), 153-170).

Commentaires: 15 pages, 8 figures (in tex format; uses pstricks)

Ref Arxiv: 0802.1035
Résumé: An even (resp. odd) lollipop is the coalescence of a cycle of even (resp. odd) length and a path with pendant vertex as distinguished vertex. It is known that the odd lollipop is determined by its spectrum and the question is asked by W. Haemers, X. Liu and Y. Zhang for the even lollipop. We revisit the proof for odd lollipop, generalize it for even lollipop and therefore answer the question. Our proof is essentially based on a method of counting closed walks.