Showing papers in "Electronic Notes in Discrete Mathematics in 2000"

TL;DR: The technique proposed may be generalized to prove additive O (1)-approximate distance labeling schemes for more general class of graphs including various intersecting classes of graphs, like chordal and circle graphs.

TL;DR: An induced matching in a graph G is a set of edges, no two of which meet a common node or are joined by an edge of G, that is, an induced matching is a matching which forms an induced subgraph.

TL;DR: This paper analyses the problems behind industrial planning and scheduling and gives a survey of possible conceptual models for scheduling problems with some planning features, comparing their advantages and drawbacks and explaining the industrial background.

TL;DR: The proposed method for finding the chromatic number of a graph G is particularly helpful when a k-coloring of anon-critical graph is known and it has to be proved that no (k-1)-colors of G exists.

TL;DR: Constraint is identified as the essential link between CLP and IP and an algorithm for bidirectional inference through these constraints is introduced and solution speed is improved over both traditional IP codes and newer mixed solvers.

TL;DR: It is proved that the graph sandwich problem for 1-join composition is NP -complete, which stands in contrast to the graph sandwiches problem for homogeneous set, which has a polynomial-time solution.

TL;DR: All Coxeter lattices are bounded, a property characterized by the fact that they are obtainable by a finite series of interval doublings, starting with the one-element lattice.

TL;DR: Weakly bipartite graphs are graphs for which some associated polyhedron is integral and are precisely the graphs which do not contain an odd K 5 minor.

TL;DR: It is discussed that many otherwise intractable problems become polynomial or linear time solvable when restricted to graphs of bounded treewidth, and some other algorithmic results that usetreewidth (e.g., applied to planar graphs) are discussed.

TL;DR: The process of exploring the space of hybrid algorithms for the problem class, and the features of ECLiPSe that enabled us to find previously undiscovered algorithms are described, pointing out the advantages of an extensible platform, such as ECL iPSe, for developing sophisticated hybrid algorithm for large scale industrial combinatorial optimisation problems.

TL;DR: This work specifies a lower bound and an upper bound of the maximum number of Hammiltonian paths that a tournament can have and two special classes of tournaments for which the number of Slater orders and Hamiltonian paths are estimated.

TL;DR: The AutoGraphiX system uses the Variable Neighborhood Search metaheuristic and data analysis methods to find extremal graphs, fixed graphs satisfying given constraints, refute conjectures, suggest conjectures and suggest proofs.

TL;DR: A new solving algorithm for Constraint Satisfaction Problems the path-repair algorithm that makes use of a repair algorithm (local search) as a basis and works on a partial instantiation in order to be able to use filtering techniques.

TL;DR: The chromatic aspects for graphs with forbidden induced subgraphs with emphasis on the question of 3-colourability are investigated and Vizing's classical edge colouring result is extended.

TL;DR: The results imply a conjecture of Hendry on the maximal number m(n, k) of edges in a graph G of order n with a unique k-factor, and it is proved that the corresponding extremal graph is unique up to isomorphism.

TL;DR: The complexity of the H -colouring problem when H is an edge coloured cycle is studied and a number of cases when the problem is polynomial time solvable and a family of NP-complete problems are identified.

TL;DR: In this paper, a characterization of S-prime graphs with connectivity 2 is given, providing a substantialy larger class of examples of such graphs as they were previously known, and a class of so-called simple S- prime graphs and a concept of extension of graphs are introduced.

TL;DR: The general problem of determining a smallest set of edges which must be added to a given graph in order to make it k-edge-connected (k-vertex-connected) is considered.

TL;DR: It is proved that a countable graph has finite clique-width iff its finite induced subgraphs haveClique- width at most k for some integer k.

TL;DR: Some old and some recent applications of tools from topology to graph coloring problems will be presented, including the use of Euler's formula and local planarity conditions, Kempe equivalence, homotopy, winding number and its higher dimensional analogues.

TL;DR: This paper surveys how the concept of crossing number, which used to be familiar only to a limited group, mostly topological graph theorists, emerges as a significant graph parameter.

TL;DR: An O(cdm+2 · (2m)d) algorithm is given to determine if a given graph is a recursive circulant graph of the form G(CDm,d), for any d ≥ 3, except in the case where c is even while d is odd.

TL;DR: The upper bound on the smallest number of cliques that cover the vertices of graph G in terms of the rank of a matrix associated with it is investigated.

TL;DR: The Ahlswede-Simonyi conjecture is proved for any fixed number of sufficiently long chains, and for the product of three chains of any length.

TL;DR: The novelty of this approach lies in the tight algorithmic integration between two sub-problems, and it suggests an elegant scheme to deal with other integrated optimization problems of the same nature.

TL;DR: This work focuses on two problems from the area of coverings of graphs, on an oriented version of Perfect Path Double Cover (PPDC) and onoriented version of Weighted Cycle Cover.

TL;DR: The problem of one-story buildings in special cases can be reduced to the planar problems and the results extended to the case of multi- story buildings are considered.

TL;DR: There are sufficient conditions for a regular multipartite graph to have a regular factor and these conditions are best possible to establish a regular graph.

TL;DR: The frame work for obtaining linear recognition algorithms for Weak bisplit graphs as well as for two sub families of this class the P-6 free bipartite graphs and the bicographs are given.

TL;DR: It is proved that for every edge-colouring of the complete graph of order n which uses exactly h(n,p) colours, there is at least one cycle of length p all whose edges have different colours.