T-graphs and the channel assignment problem

Channel Assignment and Improper Choosability of Graphs

We model a problem proposed by Alcatel, a satellite building company, using improper colourings of graphs. The relation between improper colourings and maximum average degree is underlined, which contributes to generalise and improve previous known results about improper colourings of planar graphs.

The T-join Problem in Sparse Graphs: Applications to Phase Assignment Problem in VLSI Mask Layout

Given a graph G with weighted edges, and a subset of nodes T , the T -join problem asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A i u 2 T . We describe the applications of the T -join problem in sparse graphs to the phase assignment problem in VLSI mask layout and to conformal re nement of nite element meshes. We suggest a practical algorithm ...

The T - join Problem in Sparse Graphs : Applications to Phase Assignment Problem

Given a graph G with weighted edges, and a subset of nodes T, the T-join problem asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A ii u 2 T. We describe the applications of the T-join problem in sparse graphs to the phase assignment problem in VLSI mask layout and to conformal reenement of nite element meshes. We suggest a practical algorithm for...

The ß-assignment problem in general graphs

We study a variation of the assignment problem in operations research and formulate it in terms of graphs as follows. Suppose G = (V; E) is a graph and U a subset of V. A-assignment of G with respect to U is an edge set X such that deg X (v) = 1 for all vertices v in U , where deg X (v) is the degree of v in the subgraph of G induced by the edge set X. The-assignment problem is to nd a-assignme...

A Theorem about the Channel Assignment Problem