Tel-Aviv University 1.1 The elimination tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 The elimination game • The elimination tree data structure • An algorithm • A skeleton graph • Supernodes 1.2 Applications of etrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 Efficient symbolic factorization • Predicting row and column nonzero counts •...

Tree-width and clique-width are two important graph complexity measures that serve as parameters in many fixed-parameter tractable (FPT) algorithms. The same classes of sparse graphs, in particular of planar graphs and of graphs of bounded degree have bounded tree-width and bounded clique-width. We prove that, for sparse graphs, clique-width is polynomially bounded in terms of tree-width. For p...

Many NP-complete graph problems are polynomial-time solvable on classes of bounded clique-width. Several these a hereditary class G ${\mathscr{G}}$ if they so the atoms (graphs with no clique cut-set) . Hence, we initiate systematic study into boundedness clique-width classes. A $G$ is H $H$ -free not an induced subgraph , and it ( 1 2 ) $({H}_{1},{H}_{2})$ both ${H}_{1}$ ${H}_{2}$ -free. graph...

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A cliqueindependent set is a subset of pairwise disjoint cliques of G. Denote by τC(G) and αC(G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when τC(H) = αC(H), for every induced subgraph H of G. In this paper, w...

The clique-width is known to be unbounded in the class of unit interval graphs. In this paper, we show that this is a minimal hereditary class of unbounded clique-width, i.e., in every hereditary subclass of unit interval graphs the clique-width is bounded by a constant.

This paper introduces a branch-and-bound algorithm for the maximum clique problem which applies existing clique nding and vertex coloring heuristics to determine lower and upper bounds for the size of a maximum clique. Computational results on a variety of graphs indicate the proposed procedure in most instances outperforms leading algorithms. c © 1997 Elsevier Science B.V. All rights reserved.

The maximum clique problem (MCP) is to determine a sub graph of maximum cardinality. A clique is a The corresponding optimization problem i.e. finding the maximum Maximum Clique Problem. in Handbook of Combinatorial. Common theme of every optimization problem: of semidefinite programming, A module on combinatorial optimization, Selected topics: The largest clique (i.e., complete subgraph)! In “...