Showing papers in "Journal of Combinatorial Theory, Series B in 1990"

TL;DR: The natural conjecture, formulated in several sources, asserts that the H-coloring problem is NP-complete for any non-bipartite graph H, and a proof of this conjecture is given.

TL;DR: A strengthening of Kruskal's result-Wagner's conjecture is true for all sequences in which G1 is planar, and the results of this paper will be needed for that proof.

TL;DR: It is proved that for any infinite set of graphs of bounded genus, some member of the set is isomorphic to a minor of another for any surface Σ such that a general graph may be drawn in Σ if an only if it topologically contains none of the graphs in the list.

TL;DR: This work investigates embeddings of graphs on orientable 2-dimensional surfaces such that all face boundaries have fewer edges than every noncontractible cycle and obtains a polynomially bounded algorithm for describing a minimum genus embedding with no short non-contractible cycles if such an embedding of the graph exists.

TL;DR: It is shown that either modulo (≤3)-separations, G can be drawn in a disc with no crossings except in one “small” area, and with its special vertices on the outside in the correct order.

TL;DR: It is proved that the sequence of k-subsets of V(G) is log concave and hence unimodal and these results are known for line graphs as a consequence of a result of Heilman and Lieb.

TL;DR: The method of deleted joins is used to prove that if N ( j −1) − 1 ≥ M ( p − 1) + p ( S − 1), then any coloring of the S -subsets of an N -set by M colors must yield a p -tuple of S-subsets having the same color.

TL;DR: It is proved that if G is finite and has tree-width w then it admits a tree-decomposition of tree- width ≦ w which satisfies a certain Menger-like condition.

TL;DR: It is shown that, for an infinite graph of linear growth, Kirchhoff's laws combined with the finite power condition ensures the existence and uniqueness of an electric current when a current generator is added.

TL;DR: It is easily seen that every rinite graph has such a partition, and hence by compact- ness so does any locally finite graph.

TL;DR: An O-algorithm is established which embeds a given graph isometrically into a Hamming graph (i.e., a cartesian product of complete graphs) whenever possible, and recognizes non-embeddable graphs.

TL;DR: The Four Color Theorem is equivalent to a combinatorial problem about the three-dimensional vector cross product algebra about theThree-dimensional Vector Cross product algebra.

TL;DR: It is proved that if H is a 4-uniform hypergraph with n vertices and m edges, then the transversal number τ (H) ≤ 2(m+n) 9 .

TL;DR: It is proved that the number of k × n Latin rectangles is asymptotically (n!)( n(n−1)⋯ (n−k+1) n k n (1− k n ) − n 2 e − k 2 as n → ∞ with k = o(n 6 7 ) .

TL;DR: An O((m + n)3) algorithm for deciding total unimodularity of any real m × n matrix, i.e., for deciding whether or not every square submatrix of the given matrix has determinant 0 or ±1.5.

TL;DR: This paper shows that this algorithm provides a minimum coloring and a maximum clique for any Meyniel graph by using a simple rule for choosing which nodes are to be contracted, and gives a new characterization for Meynel graphs.

TL;DR: A new hereditary class of perfect graphs G, the perfectly contractile graphs, which have the following property: Any γ(G)-colours of G can be obtained from any k-colouring of G by a sequence of switchings are defined.

TL;DR: An upper bound for the girth of the Ramanujan graphs constructed by Lubozky, Phillips, and Sarnak is established, thereby determining the asymptotic behaviour of thegirth of these graphs.

TL;DR: Theorems on the localization of the conditions of G. A. Dirac, Ore, and Geng-hua Fan are generalized to LaSalle's inequality and show that the inequality between theorems of Dirac and Ore and that of Fan and Dirac is equivalent to the same thing.

TL;DR: Several sufficient conditions on the half-degrees of a bipartite digraph are given for the existence of cycles and paths of various lengths.

TL;DR: In this article, Frank and Tardos give a good characterization of the minimum weights of paths from a fixed vertex of an undirected graph without negative circuits and a canonical packing of odd cuts with favorable properties.

TL;DR: This work presents a characterization of graphs that have small optimal overlap, and presents essentially tight bounds relating the optimal overlap to the optimal stretch.

TL;DR: A self-dual characterization is established for the matroids of S-regular subspaces which generalizes Minty's characterization of regular spaces as digraphoids.

TL;DR: A recent cycle structure theorem is used to prove that three well-known hamiltonian degree conditions each imply that a graph is either pancyclic, bipartite, or a member of an easily identified family of exceptions.

TL;DR: Grassmann graphs, Johnson graphs, a quotient of the Johnson graph, Schlafli graphs, and Gosset graphs are characterized by the above local properties and the additional conditions, without the hypotheses of parameters.

TL;DR: If T is a tournament of order n ≥n ≥n(e, k) and in T every vertex has indegree at least ( 1 4 +e)n and at most ( 3 4 − e)n then T contains the kth power of a Hamilton cycle.

TL;DR: It is shown that every l-connected graph has a vertex whose removal increases the average distance in the graph by no more than a factor of l (l−1) .

TL;DR: It is proved that every bridgeless graph has a (2, 4)-cover by four even subgraphs of total weight at most (209) w(G), which yields a weighted generalization of a result found by J. Jaeger.