Partitioning a chordal graph into transitive subgraphs for parallel sparse triangular solution

Partitioning A Chordal Graph Into Transitive Subgraphs For Parallel Sparse Triangular Solution

A Clique Tree Algorithm for Partitioning a Chordal Graph into Transitive Subgraphs

A partitioning problem on chordal graphs that arises in the solution of sparse triangular systems of equations on parallel computers is considered Roughly the problem is to partition a chordal graph G into the fewest transitively orientable subgraphs over all perfect elimination orderings of G subject to a certain precedence relationship on its vertices In earlier work a greedy scheme that solv...

Partitioning a graph into degenerate subgraphs

Let G = (V,E) be a graph with maximum degree k ≥ 3 distinct from Kk+1. Given integers s ≥ 2 and p1, . . . , ps ≥ 0, G is said to be (p1, . . . , ps)-partitionable if there exists a partition of V into sets V1, . . . , Vs such that G[Vi] is pi-degenerate for i ∈ {1, . . . , s}. In this paper, we prove that we can find a (p1, . . . , ps)-partition of G in O(|V |+|E|)-time whenever 1 ≥ p1, . . . ,...

Partitioning a Graph into Highly Connected Subgraphs

Given k ≥ 1, a k-proper partition of a graph G is a partition P of V (G) such that each part P of P induces a k-connected subgraph of G. We prove that if G is a graph of order n such that δ(G) ≥ √ n, then G has a 2-proper partition with at most n/δ(G) parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that If G is a graph of order n with minimu...

Highly Parallel Sparse Triangular Solution