Algorithm MLS (Maximal Label Search) is a graph search algorithm which generalizes algorithmsMCS, LexBFS, LexDFS andMNS. On a chordal graph, MLS computes a peo (perfect elimination ordering) of the graph. We show how algorithm MLS can be modified to compute a pmo (perfect moplex ordering) as well as a clique tree and the minimal separators of a chordal graph. We give a necessary and sufficient ...

In the graph searching problem initially a graph with all edges contaminated is pre sented We would like to obtain a state of the graph in which all edges are simultaneously clear by a sequence of moves using searchers The objective is to achieve the desired state by using the least number of searchers Two variations of the graph searching problem are considered in this paper One is the edge se...

Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those metho...

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

This paper prooves that for SSA programs the interference graph can be coloured optimally in linear time. The proof will proceed as follows: Section 2 presents some properties of SSA graphs, and the operation’s effect on creating the interference graph. Section 3 will show that the interference graph for SSA programs are chordal graphs. Section 4 will present an algorithm that can colour chorda...

In this paper we show that a very simple and efficient approach can be used to solve the all pairs almost shortest path problem on the class of weakly chordal graphs and its different subclasses. Moreover, this approach works well also on graphs with small size of largest induced cycle and gives a unified way to solve the all pairs almost shortest path and all pairs shortest path problems on di...

Graph search algorithms have exploited and in some cases identi ed graph extremities, such as the leaves of a tree and the simplicial vertices of a chordal graph. Recently, several well-known graph search algorithms have been collectively expressed as two generic algorithms called MLS and MLSM, each of which instantiates with parameters de ning the set of labels to be used, a partial order on l...

Given an arbitrary graph G = (V, E) and an additional set of admissible edges F , the Chordal Sandwich problem asks whether there exists a chordal graph (V, E ∪ F ′) such that F ′ ⊆ F . This problem arises from perfect phylogeny in evolution and from sparse matrix computations in numerical analysis, and it generalizes the widely studied problems of completions and deletions of arbitrary graphs ...

It is known that any chordal graph on n vertices can be represented as the intersection of subtrees in a tree nodes (Gavril J Comb Theory 16:47–56, 1974). This characterization has been recently used to generate random graphs by generating nodes. The space (and thus time) complexity an algorithm at least sum sizes generated subtrees. determination this was left open question Şeker et al. (Gener...