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Chvátal defined a skew partition of a graph G to be a partition of its vertex set into two non-empty parts A and B such that A induces a disconnected subgraph of G and B induces a disconnected subgraph of G. Skew partitions are important in the characterization of perfect graphs. De Figuereido et al. presented a polynomial time algorithm which given a graph… (More)

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete mul-tipartite graph or a… (More)

A fundamental problem in computational biology is the phylogeny reconstruction for a set of specific organisms. One of the graph theoretical approaches is to construct a similarity graph on the set of organisms where adjacency indicates evolutionary closeness, and then to reconstruct a phylogeny by computing a tree interconnecting the organisms such that… (More)

A lemma of Fouquet implies that a claw-free graph contains an induced C 5 , contains no odd hole, or is quasi-line. In this paper we use this result to give an improved shortest-odd-hole algorithm for claw-free graphs by exploiting the structural relationship between line graphs and quasi-line graphs suggested by Chudnovsky and Seymour's structure theorem… (More)

Reconstruction of an evolutionary history for a set of organisms is an important research subject in computational biology. One approach motivated by graph theory constructs a relationship graph based on pairwise evolutionary closeness. The approach builds a tree representation equivalent to this graph such that leaves of the tree, corresponding to the… (More)

Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric characteristic of real-life networks, namely their hyperbolicity. In smooth geometry, hyperbolicity captures the notion of… (More)

Given a set S = {C1, ..., C k } of Boolean circuits, we show how to construct a universal for S circuit C0, which is much smaller than Valiant's universal circuit or a circuit incorporating all C1,. , we embed them in a new graph D0. The embedding is such that a secure computation of any of C1, ..., C k is possible by a corresponding secure computation over… (More)

Many graph processing algorithms require determination of shortest-path distances between arbitrary numbers of node pairs. Since computation of exact distances between all node-pairs of a large graph, e.g., 10M nodes and up, is prohibitively expensive both in computational time and storage space, distance approximation is often used in place of exact… (More)

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete mul-tipartite graph or a… (More)

The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies and Research for acceptance, a thesis entitled Strictly Chordal Graphs and Phylogenetic Roots submitted by William Kennedy in partial fulfillment of the requirements for the degree of Master of Science. Abstract A phylogeny is the evolutionary history for a set of… (More)