Showing papers in "Discrete Mathematics in 1976"

TL;DR: The probability that a random graph with n vertices and cn log n edges contains a Hamiltonian circuit tends to 1 as n -> ~ (if c is sufficiently large).

TL;DR: It is shown that, for many properties P, one can find a suitable value of k such that if C"k(G) has P, then so does G, and this condition for a graph to be hamiltonian is shown to imply the well-known conditions of Chvatal and Las Vergnas.

TL;DR: The values and the number of occurences of each value of Cd(t) for several new values of d are determined for several different periods of period pn − 1.

TL;DR: An arithmetic triangle similar to Pascal's triangle is developed, interpreted in terms of numbers of pairs of nonintersecting paths in the first quadrant, with main applications about the Catalan numbers and various random walk problems.

TL;DR: The following combinatorial problem, which arose in game theory, is solved here: To find a set of vertices of a given size (in the n-cube) which has a maximal number of interconnecting edges.

TL;DR: Connections are established between characterization problems for interval graphs, circular are graphs, comparability graphs, planar lattices, 0–1 matrices, interval orders, partially ordered sets with dimension at most two, and related problems involving the representation of families of finite sets by points or intervals of the real line.

TL;DR: A t-design T=(X, B), denoted by (@l; t, k, v), is a system B of subsets of size k from a v-set X, such that each t-subset of X is contained in exactly @l elements of B.

TL;DR: In this article, it was shown that every odd dimensional projective space over the field of two elements admits a 1-packing of 1-spreads, i.e., a partition of its lines into families of mutually disjoint lines whose union covers the space.

TL;DR: This paper finds simple expressions for the first few and last few coefficients of @D"T(x) , the characteristic polynom, of D(T), of a tree T on n vertices.

TL;DR: It is shown here that for all even n(r - 1) >= 2, K(n;r) is the union of (n(r- 1) - 2)2 of its Hamilton circuits and a 1-factor, all of which are mutually edge-disjoint.

TL;DR: If every, odd cycle of length ≥5 has at least two chords, then the graph is perfect, which generalizes a result of Gallai and Suranyi and also a results of Olaru and Sachs.

TL;DR: In this note counterexamples to some questions of Grunbaum on acyclic colorings are constructed.

TL;DR: A method is described by which the enumeration of permutations of 1, 2, ... n with a prescribed sequence A of rises and falls, or a prescribe sequence B of inversions of order, is effected in terms of numbers derived from the representation theory of the symmetric group.

TL;DR: Semilattice theory is used to give an algebraic formulation of the ideas involved in the estimation of evolutionary history and to give rigorous proofs of theorems which justify certain operational procedures in current use.

TL;DR: It is shown how the study of infinite hypot raceable graphs leads to a new infinite family of finite hypotraceable graphs.

TL;DR: A set of operations on graphs which increase the number of their spanning trees is given and the following assertions are proved: a disconnected graph is “better” (it destroys less trees if removed from the complete graph) than any connected separable graph whose blocks are components of the given graph.

TL;DR: It is shown by an argument closely related to Hilbert's tenth problem (drophantine equations) that no such algorithm exists and any combinatorial optimization problem can be formulated as an IP problem if its feasible region S is finite.

TL;DR: The middle graph M(G) of G is hamiltonian if and only if G contains a closed spanning trail and if G is connected and without points of degree =< 1.

TL;DR: It is proved that there are only finitely many irreducible graphs with a given achromatic number, and all graph with a chromatic number less than four are described.

TL;DR: A complete classification is given for non-neighborly combinatorial 3-manifolds with nine vertices and it is shown that 1057 of those spheres are polytopal, i.e. can be realized as boundary complexes of convex 4-polytopes.

TL;DR: The voltage graph construction of Gross is extended and methods are applied to derive both orientable and non-orientable genus embeddings for some families of complete tripartite graphs.

TL;DR: A new parameter, the maximum number of disjoint independent dominating sets in G, is studied and the class of graphs whose vertex sets partition intoindependent dominating sets is investigated.

TL;DR: This paper verifies the truth of the conjecture that all critical graphs have odd order for all graphs of order less than 12 and all graph of order 12 and maximum degree 3 and determines all critical graph through order 7.

TL;DR: In this paper are described certain geometric constructions, which are applied to obtain projectively unique polytopes from ones of lower dimension; in particular, they lead to projectivelyunique poly topes with many vertices.

TL;DR: The purpose of this paper is to discuss several invariants each of which provides a measure of the intuitive notion of complexity for a finite partially ordered set.

TL;DR: It is shown that if m=min {d(x)+d(y): [x, y]@?E} then G=(V, E) is a block of order n, different from K"n".

TL;DR: Necessary and sufficient conditions under which a given finite sequence of pairs of integers can realize a graph are found and are extended to diagraphs.

TL;DR: In this paper, the authors established necessary and sufficient conditions for bounded-integer MIMM representability for piecewise-linear functions of a single real variable, and the utility of a mixed integer minimization model (MIMM) as well as its relationship to classes of piecewise linear functions of n variables was described.

TL;DR: It is proved that the poset P consisting of all induced connected subgraphs of a nontrivial connected graph G, partially ordered by inclusion, has dimension n where n is the number of noncut vertices in G whether or not P is a lattice.