Showing papers in "Discrete Mathematics in 1994"

TL;DR: The concept of a Riordan array is used in a constructive way to find the generating function of many combinatorial sums, which can help to obtain the closed form of the sum or its asymptotic value.

TL;DR: It is shown that the necessary and sufficient condition for a cyclic code C of length n to be an LCD code is that the generator polynomial g(x) of C be self-reciprocal and all the monic irreducible factors of g(X) have the same multiplicity in g( x) as in xn-1.

TL;DR: Two kinds of graph polynomials are introduced, clique polynomial and independent setPolynomial, and expansions of these polynmials are focused on.

TL;DR: If a class of graphs has the property that all facets of the stable set polytope can be generated this way in a bounded number of setps, then thestable set problem is polynomially solvable for these graphs.

TL;DR: This work studies the case in which all these components of a graph are different from a tree whose order is not greater than n, and some sufficient conditions for a graph to have the maximum possible conditional connectivity.

TL;DR: The relationship between λ(G) and another graph invariant, the path covering number of Gc, is derived and applications include the determination of the λ-number of the join of two graphs, the product of two complete graphs, and the complete multi-partite graphs.

TL;DR: The main focus of this part of the survey is on recent results that are related to the basic problems of computing, approximating, or measuring the convex sets which are the smallest that contain a given convex body K or are the largest contained in K.

TL;DR: The sum of distances between all pairs of vertices in these composite graphs is computed.

TL;DR: How the property of n-extendability interacts with such other graph parameters as genus, toughness, claw-freedom and degree sums and generalized neighborhood conditions is described and the behavior of matching extendability under the operation of Cartesian product is investigated.

TL;DR: The relations among various combinatorial conjectures are discussed, to wit: A conjecture of J. Dinitz on partial Latin squares, closely related to a conjecture of N. Alon and M. Tarsi on Latin squares.

TL;DR: An infinite class of graphs each of whose bondage number is greater than its maximum degree plus one is presented, thus showing a previously conjectured upper bound to be incorrect.

TL;DR: The graphs with bounded path-width and with bounded proper-path-width are investigated and the minimal acyclic forbidden minors are characterized for these families of graphs.

TL;DR: A generalization of Wilson's fundamental construction for group divisible designs which is intended to produce 3-wise balanced designs, rather than pairwisebalanced designs, is discussed.

TL;DR: It will be shown that any two triangulations of a closed surface can be transformed into each other by flipping diagonals in quadrilaterals if they have a sufficiently large and equal number of vertices.

TL;DR: The correspondence of groups and polytopes is used to construct infinite series of chiral and regularpolytopes whose facets or vertex-figures are chiral or regular toroidal maps.

TL;DR: The unifying role of the hypergeometric nature of binomial identities is underlined, which is basic for combinatorial models and techniques, developed during the last decade, and for the recent algorithmic proof procedures.

TL;DR: It is proved that the problem of determining the total chromatic number of a k-regular bipartite graph is NP-hard, for each fixed k⩾3.

TL;DR: It is proved that contractible transformations do not change the homology groups of graphs and this paper continues to study properties of contractable transformations of graphs.

TL;DR: It is proved that quadratic fractional isomorphicism is the same as isomorphism and semi-isomorphism is related to is morphism of bipartite graphs.

TL;DR: The problems (R) and (U) for the degree sequence and the size sequence of induced subgraphs for undirected and directed graphs are discussed, concentrating on the complexity of the corresponding decision problems and their connection to a natural search problem on graphs.

TL;DR: The integral sum number of the small graphs is found and it is seen that all paths and all matchings are integral sum graphs.

TL;DR: It is shown that every k -regular k -connected graph on n vertices has k -diameter at most n /2 and this upper bound cannot be improved when n =4 k −6+ i (2 k −4).

TL;DR: It turns out that for every n ϵ N Tamari lattices and their congruence lattices have the same number of elements and theSame number of coverings, both connected with the Catalan numbers.

TL;DR: It is shown that if k⩾2 and k∤d(v) (∀vϵV(G)) and G is a simple graph, then G has an equitable edge-colouring with k colours, and this result is extended to one about I-regular edge-colourings of simple graphs.

TL;DR: In this article, the notion of doubling fixed points in the graph of an exceeding mapping was used to give new combinatorial interpretations for the Euler finite-difference tableau relating the sequence n! to the sequence of derangement numbers.

TL;DR: In this paper, the concept of genus distribution of graphs is generalized to include nonorientable imbeddings and explicit computations of the total imbedding distributions for several interesting graph classes are given.

TL;DR: An expansion for a certain determinant that involves two sets of formal variables is derived that provides a unified approach to several known expansions including a generalized form of the matrix-tree theorem.

TL;DR: A generalized data structure called graph-driven binary decision diagram, which allows for many important functions a representation of polynomial size, even for functions whose representations by OBDDs have exponential size, is presented.

TL;DR: A brief report on some interesting theorems and their interconnections and the key result, though found already in 1935, was almost forgotten and its original proof remained unnoticed until very recently.

TL;DR: It is shown that there is a graph L with n vertices and at least n1.36 edges such that it contains neither L 3 nor K 2, 3 but every subgraph with 2n 4 3 (log n) 2 edges contains a C 4, (n > n O ) .