Showing papers in "Discrete Mathematics in 1999"

TL;DR: This work gives O(n+m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph and linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparable graphs and their complements.

TL;DR: The authors proposed an algorithm that stabilizes and accelerates the solution process while remaining within the linear programming framework, which can be used to improve the solution times for difficult instances and to solve larger ones.

TL;DR: An elementary technique is used for the enumeration of Dyck paths according to various parameters for several of the considered parameters the generating function is expressed in terms of the Narayana function.

TL;DR: This paper describes a systematic approach to the enumeration of ‘non-crossing’ geometric congurations built on vertices of a convex n-gon in the plane that relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation.

TL;DR: This paper defines a slightly different Markov chain, and presents a very simple proof of its rapid mixing, using the method of path coupling, which significantly improves the previous best bound for this problem, which was a bound of O( n 5 log n ), for the Karzanov and Khachiyan chain.

TL;DR: It turns out that for all d ⩾ 2 and for a prescribed but arbitrary set of m ⩽ 2 pairwise nonparallel lattice directions, the problems are solvable in polynomial time if m = 2 and are NP-complete (or NP-equivalent) otherwise.

TL;DR: A survey of recent results on the notion of symbolic complexity, which counts the number of factors of an infinite sequence, particularly in view of its relations with dynamical systems.

TL;DR: The study of a variation of standard domination, namely restrained domination, is initiated and it is shown that the decision problem for γ r ( G ) is NP-complete even for bipartite and chordal graphs.

TL;DR: The generating function also enumerates certain lattice paths, plane trees, and directed animals, giving hope that these areas of combinatorics can be applied to enumerating permutations with excluded subsequences.

TL;DR: Partition representable matroids are shown to be closely related to generalized quasigroup equations read out of the matroid structure and a special morphism of partition representations, called partition isotopy, is introduced.

TL;DR: In this paper, it was shown that any irreducible T-module W is both thin and dual-thin in the sense of Terwilliger, and that the isomorphism class of W is determined by two parameters, the endpoint and diameter of W.

TL;DR: The links between o( G ) and mad( G) defined as the maximum average degree of the subgraphs of G are studied.

TL;DR: It is concluded that the game chromatic number of a planar graph is at most 30, which improves the previous known upper bound for the gamechrome number of planar graphs.

TL;DR: A short proof is given that the graphs with proper interval representations are the same as theGraphs with unit interval representations.

TL;DR: Answering a question from Bollobas and Erdos (Graphs of external weights, to appear), wi(m) for every m is determined and bounds for the case α ≠ 1.

TL;DR: It is shown that ( B n ) is the unique sequence of real numbers such that det A n = det B n =n!! for all n, where n

TL;DR: A unified overview of Catalan, Motzkin, and R -numbers is presented, intended as a primer of sequences and techniques, combinatorial structure and recursion, generating function equations, difference triangles, and Lagrange inversion.

TL;DR: Convexity invariants like Caratheodory, Helly and Radon numbers are computed for triangle path convexity in graphs like Helly, Radon and Carathodory.

TL;DR: This paper strengthens and expands Justesen's result, showing that if d ( x )+ d ( y )⩾4 k −1 for every pair of non-adjacent vertices x and y of G , then G contains k vertex-disjoint cycles.

TL;DR: In this article, the concept de personnalite de la marque is proposed and an adaptation of the concept of personnality of the marche is presented, in the context of a contexte francais de l’echelle de Personnalité de the marque, mise au point par Jennifer Aaker.

TL;DR: It is able to show that when n is representable then it is almost surely representable with min(a, b) small, with an explicit bound.

TL;DR: The Shi arrangement Ln is the arrangement of affine hyperplanes in R n of the form xi − xj = 0 or 1, for 1 ⩽ i R n into (n + 1)n−1 regions, as was first proved by Shi as discussed by the authors.

TL;DR: It is shown that if G is a graph such that the maximum size of a set of pairwise edge-disjoint triangles is v(G), then there is a set C of edges of G of size at most (3 − e)v(G) such that E(T) ∩ C ≠ ∅ for every triangle T of G, where e > 3 23 .

TL;DR: It is proved that every 2-connected claw-free and P7-free, or claw- free and Z4- free, or claws and eiffel-free graph is either hamiltonian or belongs to a certain class of exceptions.

TL;DR: An involution is introduced in the set of all Dyck paths of semilength n from which one re-obtains easily the equidistribution of the parameters ‘number of valleys’ and ‘ number of doublerises’.

TL;DR: It is shown that this multilinear polynomial can be extended to include further families of homeomorphic graphs, and derive some properties of its coefficients.

TL;DR: The circular chromatic numbers of Mycielski's graphs are investigated and are proved to be circular.

TL;DR: It is shown that the order complex of the direct product of two posets is collapsible (resp., non-evasive) if the ordercomplex of each factor is collapsibles (resp, non-Evasive).

TL;DR: The q -analogs of several classical binomial coefficient congruences due to Babbage, Wolstenholme and Glaisher turn out to be succinct and unexpected.

TL;DR: Some lower bounds of the signed domination number of a graph are obtained, and it is shown that these lower bounds are sharp, and this result is extended in Dunbar et al. (1995).