Showing papers in "Journal of Combinatorial Theory, Series A in 1967"

TL;DR: In this article, a study of the combinatorial properties of the dichromatic polynomials of graphs, especially those properties theoretically applicable to the recursive calculation of the polynomial, is made.

TL;DR: The number β is a geometric invariant, like μ, but is also a duality invariant as discussed by the authors, and provides a complete determination of separability for matroids.

TL;DR: In this paper, a class of nonlinear Boltzmann-like equations are interpreted from a probabilistic point of view, leading to an exponential formula for the solution, which, in the special cases considered, can be made explicit by algebraic and combinatorial considerations involving derivations of an associated algebra and exponentials of these and a (commutative but possibly nonassociative) multipliaction on a dual of this algebra.

TL;DR: In this article, the eigenvalues of the adjacency matrices of point-symmetric graphs with a prime number of points are characterized and group-graphs are defined.

TL;DR: An enumeration of all the different combinatorial types of 4-dimensional simplicial convex polytopes with 8 vertices is given in this paper, which corrects an earlier enumeration attempt by M. Bruckner, and leads to a simple example of a diagram which is not a Schlegel diagram.

TL;DR: In this article, the authors investigated the extent to which line symmetry and regularity imply point symmetry, and gave some conditions on the number of points and the degree of regularity.

TL;DR: The Burnside ring of G is a semisimpleteness algebra over Q and formulas for certain primitive idempotents of this algebra yield the theorem of Artin on rational characters.

TL;DR: The so-called "birthday surprise" is the fact that, on the average, one need only stop about 24 people at random to discover two who have the same birthday.

TL;DR: In this paper, the authors investigate properties of a general notion of independence and use some of the results obtained to solve certain problems in combinatorial analysis concerned with the existence of systems of representatives.

TL;DR: In this paper, an expository article describes work which has been done on various problems involving infinite graphs, mentioning also a few unsolved problems or suggestions for future investigation, including the problem of infinite graphs.

TL;DR: In this article, the authors propose a systeme ordonnes finis, in which a set of parenthesages and transformations of monomes non-associatifs are organized in a system.

TL;DR: In this paper, a solution to the problem of characterizing graphs that have at least one square root graph is presented, which is stated in terms of existence of a set of complete subgraphs of the given graph satisfying certain properties.

TL;DR: In this paper, the authors give three different ways of producing the one-to-one correspondence between planted plane trees and trivalent planted planes discovered by Harary, Prins, and Tutte.

TL;DR: In this article, a combinatorial theorem on simplicial maps from an orientable n-pseudomanifold into an m -sphere with the octahedral triangulation is proved.

TL;DR: In this article, the number of idempotent elements in the symmetric semigroup on n elements has been investigated and a number of combinatorial identities and congruences are given.

TL;DR: In this article, the problem of determining the minimal k for which a set of 5-tuples exists such that for each x in N there is an element in N that differs from x in at most one coordinate is treated.

TL;DR: In this article, the following theorem is proved and generalized: the partitions of any positive integer, n, into parts of the forms 6 m +2, 6 m+3, 6m +4 are equinumerous with those partitions of n into parts ≧2 which neither involve sequences nor allow any part to appear more than twice.

TL;DR: The thickness of the n-dimensional cube-graph Wn is t (W n ) = { n + 1 4 } as mentioned in this paper, where W n is the number of vertices in the cube graph.

TL;DR: A tetrahedral graph is defined as a graph G whose vertices may be identified with the n(n−1)(n−2)/6 unordered triplets on n symbols, such that two vertices are adjacent if and only if the corresponding triplets have two symbols in common.

TL;DR: The main result of as discussed by the authors is that every 2-connected graph with a 1-factor has more than one cycle if and only if there is a cycle of even length whose edges are alternately in and not in the given 1-Factor.

TL;DR: In this paper, the following theorems of Erdos, Ginzburg, and Ziv are proved: o (1) Let A⊕B=A∪B∪(A+B) ∪(B+B), if G is a finite Abelian group and A 1 +…+A k subsets of G with |A 1 |+…+|A k |≥|G|, then either A 1 ⊕⌉A k =G or 0∈A 2 +… +A k

TL;DR: In this paper, a simple formula for the number of subtrees of the arc digraph of a directed graph was given in terms of the total number of trees of the graph.

TL;DR: In this paper, the following theorems are proved: (1) if α1, …, α2p−1 are distinct and not zero, then every element of G is a sum over a subsequence of S and if p>2 then 0 is the sum of a subsequences of α 1,..., α 2p−2.

TL;DR: In this paper, the genus of the complete graph with 12 s vertices was determined by using a non-Abelian group to identify the vertices, which is a novel approach for orientable 2-manifolds.

TL;DR: In this article, the color patterns that are invariant under a given permutation of the colors of a set D into a set R, where equivalence is defined by means of a permutation group G acting on D.