Algorithms for generalized vertex-rankings of partial k-trees

Generalized Vertex-Rankings of Partial k-trees

Md. Abul Kashem 1, Xiao Zhou 2 and Takao Nishizeki 1 1 Graduate School of Information Sciences z Education Center for Information Processing Tohoku University, Senda2 980-77, 3apan. E~aail : [email protected], [email protected] [email protected] Abst ract . A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such ...

Algorithms for Vertex Partitioning Problems on Partial k-Trees

In this paper, we consider a large class of vertex partitioning problems and apply to them the theory of algorithm design for problems restricted to partial k-trees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications. We give a precise characterization of vertex partitioning problems,...

Algorithms for the Multicolorings of Partial k-Trees

Let each vertex v of a graph G have a positive integer weight ω(v). Then a multicoloring of G is to assign each vertex v a set of ω(v) colors so that any pair of adjacent vertices receive disjoint sets of colors. A partial k-tree is a graph with tree-width bounded by a fixed constant k. This paper presents an algorithm which finds a multicoloring of any given partial k-tree G with the minimum n...

Vertex rankings of chordal graphs and weighted trees

In this paper we consider the vertex ranking problem of weighted trees. We show that this problem is strongly NP-hard. We also give a polynomial-time reduction from the problem of vertex ranking of weighted trees to the vertex ranking of (simple) chordal graphs, which proves that the latter problem is NP-hard. In this way we solve an open problem of Aspvall and Heggernes. We use this reduction ...

Vertex Equitable Labelings of Transformed Trees