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We study the decomposition conjecture posed by Barát and Thomassen (2006), which states that, for each tree T , there exists a natural number k T such that, if G is a k T-edge-connected graph and |E(T)| divides |E(G)|, then G admits a partition of its edge set into classes each of which induces a copy of T. In a series of papers, starting in 2008, Thomassen… (More)

A P-decomposition of a graph G is a set of pairwise edge-disjoint paths of G with edges that cover the edge set of G. Kotzig (1957) proved that a 3-regular graph admits a P 3-decomposition if and only if it contains a perfect matching, and also asked what are the necessary and sufficient conditions for an-regular graph to admit a P-decomposition, for odd.… (More)

In 2006, Barát and Thomassen posed the following conjecture: for each tree T , there exists a natural number k T such that, if G is a k T-edge-connected graph and |E(G)| is divisible by |E(T)|, then G admits a decomposition into copies of T. This conjecture was verified for stars, some bistars, paths of length 3, 5, and 2 r for every positive integer r. We… (More)

- JOÃO DA SILVA, GOMES MOTA, AResumo da dissertação
- 2002

A Localização é um elemento essencial na generalidade das plataformas móveis dado que é necessário ter uma estimativa rigorosa da posição e orientação em relação ao mapa do ambiente onde opera a palataforma para cumprir a maioria das missões. A so-lução proposta foi desenvolvida no âmbito do projecto RESOLV, cujo objectivo principal é criar modelos… (More)

Let H be an orientation of a graph H. Alon and Yuster proposed the problem of determining or estimating D(n, m, H), the maximum number of H-free orientations a graph with n vertices and m edges may have. We consider the maximum number of H-free orientations of typical graphs G(n, m) with n vertices and m edges. Suppose H = C is the directed cycle of length… (More)