The all-pairs-shortest-length (APSL) problem of a graph is to nd the lengths of the shortest paths between all pairs of vertices. In this paper, we study the APSL problem on chordal bipartite graphs. By a simple reduction, we show that solving the APSL problem on chordal bipartite graphs can be transformed to solving the same problem on certain strongly chordal graphs. Consequently, there is an...

The interference graph for a procedure in Static Single Assignment (SSA) Form is chordal. Since the k-colorability problem can be solved in polynomial-time for chordal graphs, this result has generated interest in SSA-based heuristics for spilling and coalescing. Since copies can be folded during SSA construction, instances of the coalescing problem under SSA have fewer affinities than traditio...

We characterize clique trees of a chordal graph in their relation to simplicial vertices and perfect sequences of maximal cliques. We investigate boundary cliques de ned by Shibata[23] and clarify their relation to endpoints of clique trees. Next we de ne a symmetric binary relation between the set of clique trees and the set of perfect sequences of maximal cliques. We describe the relation as ...

An acyclic coloring of a graph is a proper vertex coloring without bichromatic cycles. We show that the acyclic colorings of any weakly chordal graph G correspond to the proper colorings of triangulations of G. As a consequence, we obtain polynomial-time algorithms for the acyclic coloring problem and the perfect phylogeny problem on the class of weakly chordal graphs. Our results also imply li...

The oriented diameter of a bridgeless connected undirected (bcu ) graph G is the smallest diameter among all the diameters of strongly connected orientations of G. We study algorithmic aspects of determining the oriented diameter of a chordal graph. We (a) construct a linear-time approximation algorithm that, for a given chordal bcu graph G, finds a strongly connected orientation of G with diam...

A cycle C of length k is extendable if there is a cycle C′ of length k+1 with V (C) ⊂ V (C′). A graph G = (V,E) of order n is cycle extendable when every cycle C of length k < n is extendable. A chordal graph is a spider intersection graph if it admits an intersection representation which consists of subtrees of a sub-divided star (or spider). In 1990, Hendry conjectured that all hamiltonian ch...

A block graph is a graph whose blocks are cliques. A block duplicate (BD) graph is a graph obtained by adding true twins (i.e., adjacent vertices with the same closed neighborhood) to vertices of a block graph. If each cut-vertex belonging to three or more blocks in the block graph receives at most one true twin, the resulting graph is called a restricted block duplicate (RBD) graph. BD and RBD...

In this paper we consider a fundamental problem in the area of viral marketing, called TARGET SET SELECTION problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the TARGET SET SELECTION problem can be solved in linear time, which generalizes Chen’s result [2] for trees, and the time c...

In this paper, we first prove that when the associated graph of a polynomial set is chordal, particular triangular computed by general algorithm in top-down style for computing decomposition has an as subgraph chordal graph. Then Wang's method and subresultant-based regular style, all sets appearing process with any these algorithms have graphs subgraphs These theoretical results can be viewed ...

A graph is ptolemaic if and only if it is both chordal and distancehereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). ...