Showing papers in "Discrete Mathematics in 1985"

TL;DR: An O( nm )-time algorithm for finding a decomposition of an n -vertex, m -edge graph is given and it is described how this decomposition can be used in divide-and-conquer algorithms for various graph problems, such as graph coloring and finding maximum independent sets.

TL;DR: Two invariants of the family of interval orders that agree with an interval graph are established, namely magnitude, which affects end-point placements, and the property of having the lengths of all representing intervals between specified bounds.

TL;DR: It is proved that for any graph, the interval thickness of a graph G is the minimum clique number over any interval supergraph of G and the node-search number is the least number of searchers required to clear the ‘contaminated’ edges of agraph.

TL;DR: The hull number ( h ) of a graph is the cardinality of the smallest set of points whose convex hull is the entire graph, which is the smallest convex set that contains T.

TL;DR: The principal result (Theorem 2) provides necessary conditions for the existence of a homomorphism onto a prescribed target and it is shown that iterated cartesian products of the Petersen graph form an infinite family of vertex transitive graphs no one of which is the homomorphic image of any other.

TL;DR: It is proved that χ can be bounded by a function of ω for two well-known relatives of interval graphs.

TL;DR: Most of the problems and results concern the relation between the clique-cover number and stability number, or between the chromatic number and clique number of these graphs.

TL;DR: It is proved that the 2-amalgam of perfect graphs is perfect, a new graph composition that generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations.

TL;DR: A 4-parametric family of 3-manifolds which includes the lens spaces and Poincare's sphere is introduced and the proof that every 3- manifold can be represented by a | G | is somewhat simpler than the original based on K ( G ): it is a direct consequence of the triangulation theorem.

TL;DR: On presente une interpretation combinatoire de l'algebre des matrices et on donne des demonstrations de cinq identites matricielles classiques.

TL;DR: A characterization is presented here showing when a path graph is an EPT graph and it is proved that it is an NP-complete problem to recognize whether a graph is a EPT graphs.

TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.

TL;DR: By producing a monadic sentence which codes arithmetic on n with probability μ = 1, it is shown that every recursive real is μ(θ) for some monadic θ, and the 0–1 law can fail if monadic quantification is allowed in defining the sentence θ.

TL;DR: Pairs of binary linear codes C 1, C 2 with the property that for any nonzero c 1 e C 1 and c 2 e C 2 , there are coordinates in which both c 1 andc 2 are nonzero are studied.

TL;DR: A characterization of circle graphs is derived which yields a polynomial time recognition algorithm and a combinatorial relationships between such an orientation and such a double labelling is studied.

TL;DR: It is shown that if A is a family of n convex and pairwise disjoint segments in the plane then the number of geometric permutations formed by all common transversals of A cannot be more than n.

TL;DR: First a point insertion theorem is proved and a representation theorem for such relation algebras is deduced by inherently relational methods, simplifying the proof of a similar result from Jonsson, Maddux and Tarski.

TL;DR: It is shown that strong unique independence graphs and unique independence trees are characterized by having a unique maximum independent set and being independent of the complement.

TL;DR: A theorem which relates S 1 ( n, k, λ ∥ θ ) and S ( n , k , λ∥θ ) to each other, and to other special numbers, is proved and provides a unified approach to a number of special cases which have recently appeared in the literature.

TL;DR: It is shown that a set of three orthogonal partitioned incomplete Latin squares of type 2 n exists for all odd n > 3; and for all even n > 38, except possibly n = 42, 44, 48, 52, 54, and 80.

TL;DR: This paper solves 3 of the 6 problems of A. Kotzig on regular and strongly-regular self-complementary graphs, mentioned in “Graph Theory and Related Topics” edited by J.A. Bondy and U.S.R. Murty.

TL;DR: Graphs called senders are developed here, used to prove a number of theorems about the class of minimal F, as well as various related results.

TL;DR: Supplementary difference sets 2{12n; k, r; λ} are used to construct D-optimal designs for n ≡ 2 mod 4, where k,r, λ are defined through n.

TL;DR: A non-constructive proof of the existence of good coverings of binary and non binary Hamming spaces by spheres centered on a subspace (linear codes) is given.

TL;DR: This approach provides a conceptually simpler proof of Anstee's related result and yields the structural description of totally balanced hypergraphs.

TL;DR: The main result is generalized for classes in which the assignment of sets to vertices must be one-to-one, as well as for classes of simplicial complexes arising as nerves of sets from a pre-specified family.

TL;DR: Alon and Gyori have obta ined proofs of the best possible upper bound for it, namely nk, and provide another different but very simple proof of this last result.

TL;DR: This paper considers the problem of finding two disjoint directed paths with prescribed ends in an acylic digraph by reducing it to a problem of planarity testing of an undirected graph and proves the conjecture of Allender that a digraph of order n and girth g ⩾ 4 has at most 2 n − g shortest cycles.