Displaying similar documents to “Drawing planar graphs with large vertices and thick edges.”

Light edges in 1-planar graphs with prescribed minimum degree

Dávid Hudák, Peter Šugerek (2012)

Discussiones Mathematicae Graph Theory

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A graph is called 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree δ ≥ 4 contains an edge with degrees of its endvertices of type (4, ≤ 13) or (5, ≤ 9) or (6, ≤ 8) or (7,7). We also show that for δ ≥ 5 these bounds are best possible and that the list of edges is minimal (in the sense that, for each of the considered edge types there are 1-planar graphs whose set of types of edges contains...

The Capacitated Arc Routing Problem. A heuristic algorithm.

Enrique. Benavent, V. Campos, Angel Corberán, Enrique Mota (1990)

Qüestiió

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In this paper we consider the Capacitated Arc Routing Problem, in which a fleet of K vehicles, all of them based on a specific vertex (the depot) and with a known capacity Q, must service a subset of the edges of the graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity. A heuristic algorithm for this problem is proposed consisting of: the selection of K centers, the construction of K connected graphs with associated loads...