Showing papers in "Discrete Applied Mathematics in 1984"

TL;DR: It is shown that there are graphs on which arbitrarily many cops are needed to catch the robber and it is proved that for planar graphs 3 cops always suffice to win.

TL;DR: 3-SAT is NP-complete when restricted to instances where each variable appears in at most four clauses, and SAT may be solved in linear time.

TL;DR: This paper shows that the greedy algorithm finds a solution with value at least 1/(1 + α) times the optimum value, where α is a parameter which represents the ‘total curvature’ of Z, and can prove the optimality of the greedy algorithms even in instances where Z is not additive.

TL;DR: It is shown that any two such embeddings of the same graph G are essentially the same, and a polynomial-time algorithm is given which will find such an embedding if it exists.

TL;DR: This paper investigates the complexity status of these problems on various sub-classes of perfect graphs, including comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees, where the k-cluster problem is polynomial and the weighted and connected versions are studied.

TL;DR: Polynomial algorithms to locate minimum weight dominating sets and independent dominating sets in strongly chordal graphs and to efficiently solve certain optimization problems for totally balanced matrices are presented.

TL;DR: Completing partial Latin squares is shown to be NP-complete using a reduction from partitioning tripartite graphs into triangles using classical embedding techniques of Hall and Ryser.

TL;DR: It is shown that unlabeledPlanar graphs can be encoded using 12 n bits, and an asymptotically optimal representation is given for labeled planar graphs.

TL;DR: It is shown that no deterministic protocol exists which is fair and results in at most n − 1 cuts and a deterministic fair protocol with 4 cuts for n =4 is proposed.

TL;DR: The aim of this paper is to investigate the mutual relationship of the metric and the ordinal/ combinatorial approaches to the median problem in the class of median graphs and establish (i) and (ii) for arbitrary median graphs.

TL;DR: In this article, the authors considered the problem of finding a maximum area rectangle that is fully contained in a given rectangle A and does not contain any point of S in its interior.

TL;DR: It is shown that if the points of S are drawn randomly and independently from A , the problem can be solved in O( n (log n ) 2 ) expected time.

TL;DR: It is shown that with a four letter alphabet the largest unavoidable repetitions in arbitrarily long words are of the form uvu where the length of uvu is 75th of the lengthof uv.

TL;DR: A compact subspace of Euclidean space related to the behavior of L under iteration is defined and it is seen that this subspace can have fractional Hausdorff dimension.

TL;DR: In this article, a method for transforming an indefinite 0-1 quadratic programming problem into an equivalent positive definite problem of precisely the same size is described. But this technique is combined with a system of analytical bounds on the variables.

TL;DR: A number of sub-classes of this problem are distinguished, arising out of whether or not a dendrogram is considered to be binary, labelled and ranked, and results are reviewed for each.

TL;DR: The interval number i(G) of a graph G is the smallest number t such that G has a t-representation, and it is proved that, for any fixed value of t with t≥2, determining whether i( G)≤t is NP-complete is NP -complete.

TL;DR: This work solves a bipartition problem for cubic graphs using the Laplace Operator on compact Riemann surfaces with good results on both the horizontal and the vertical.

TL;DR: The sphericity of a graph G is defined to be the minimum number n such that G is isomorphic to a space graph in n-space.

TL;DR: A negative answer to the question if it is true that c(G) ≤ k whenever the maximal degree of G is at most k is given by showing that, for all positive integers k, n (k ≥ 3), there exists a k-regular graph G with c( G) ≥ n.

TL;DR: In this paper, the properties of perfect elimination orderings in chordal graphs are investigated and the connections between convex subsets and quasiconcave functions in a graph are discussed.

TL;DR: The speed-up of this algorithm is optimal in the sense that the depth of the algorithm is of the order of the running time of the fastest known sequential algorithm over the number of processors used.

TL;DR: In this paper, the relation of generic rigidity to Laman's theorem has been investigated, where the matroids were defined on the set of velocities of the joints.

TL;DR: It is shown that questions concerning the complexity of approximation algorithms for the Maximum Independent Set and Minimum Vertex Cover Problems are at least as hard as a sample of other open questions concerning approximating NP-hard problems, including Graph Coloring, Set Covering and Dominating Set Problems.

TL;DR: Algebraic structures of line drawings are elucidated, and a necessary and sufficient condition is obtained for a line drawing to represent a polyhedron, and the class of pictures that represent nontrivial three-dimensional configurations when vertices are drawn in general position is characterized by incidence structures of polyhedra.

TL;DR: The algorithm is based on the simplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian cycle.

TL;DR: Three methods for describing differences in the order of the endpoints of the intervals along the line are given and it is shown how these methods can be used to determine whether a graph has a representation satisfying various restrictions on the relative positions of the interval.

TL;DR: This paper addresses the question of determining the class of rectangular matrices having a given graph as a row or column graph, and presents a method of determining when an inverse is minimal.

TL;DR: In this paper, a sufficient condition for a copy language to be regular is provided; an application of this condition is demonstrated in the context of regular copy language construction, where the copying relation copy∗ is defined as the reflexive and transitive closure of copy, and a copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵ Σ + : w copy ∗ z}, it is referred to as a copy languages.