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Showing papers in "Journal of Combinatorial Theory, Series B in 1995"


Journal ArticleDOI
TL;DR: An algorithm, which for fixed k ≥ 0 has running time O (| V(G) | 3 ), to solve the following problem: given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs.

1,438 citations


Journal ArticleDOI
Fred Galvin1
TL;DR: This paper generalizes Janssen′s result on complete bipartite graphs Km, n with m ≠ n and answers a question of Dinitz about the list chromatic index.

328 citations


Journal ArticleDOI
TL;DR: It is proved that Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges.

212 citations


Journal ArticleDOI
TL;DR: It is proved that every planar graph of girth at least 5 is 3-choosable and it is even possible to precolor any 5-cycle in the graph.

178 citations


Journal ArticleDOI
TL;DR: The main result is actually a new min-max theorem concerning "bisupermodular" functions on pairs of sets, which implies the node-connectivity augmentation theorem as well as a generalization of an earlier result of the first author on the minimum number of new directed edges whose addition makes a digraph k-edge-connected.

130 citations


Journal ArticleDOI
TL;DR: In this paper, a new min-max formula for the minimum number of new edges to be added to a given directed graph to make it k-node-connected was derived, which gives rise to a polynomial time algorithm.

120 citations


Journal ArticleDOI
TL;DR: A polynomial-time approximation algorithm is presented which makes a k -connected graph ( k + 1)-connected by adding a new set of edges with size at most k − 2 over the optimum.

99 citations


Journal ArticleDOI
TL;DR: The minimum number of edges sufficient for the existence of k triangles intersecting in exactly one common vertex is determined.

84 citations


Journal ArticleDOI
Fan Chung1, Ron Graham1
TL;DR: The cover polynomial C(D; x, y) for a directed graph D is introduced and its relationships to other graph polynomials are examined.

80 citations


Journal ArticleDOI
TL;DR: For 0 0, there exists a real constantC=C(l, η), such that almost every random graphGn, p with p withp=p(n)≥Cn−1+1/2l satisfies Gn,p→ 1/2+ηC2l+1.

78 citations


Journal ArticleDOI
TL;DR: Any bridgeless cubic graph G having a 2-factor with at most two odd components has a 5-cycle double cover and there exists a collection L of five Eulerian subgraphs of G such that every edge of G is an edge of exactly two sub graphs in L.

Journal ArticleDOI
TL;DR: The objective here is to study the effect on the metric and on the "representativeness" of making local changes in the drawing or in the surface of a graph drawn on a connected surface Σ.

Journal ArticleDOI
TL;DR: A simple proof of the fact that for a wide variety of classes of maps on surfaces, almost all maps in the class are asymmetric is given.

Journal ArticleDOI
TL;DR: This paper proves the conjecture made by O. V. Borodin in 1976 that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degnerate graph, that is, a forest.

Journal ArticleDOI
TL;DR: A method to generate all local tournaments by performing some simple operations on some simple basic oriented graphs is described and a description of all local tournament with the same underlying proper circular are graph is obtained.

Journal ArticleDOI
TL;DR: It is proved that for any ϵ > 0, there exists a number m, depending only on ϵ, such that if δ( G ) ≥ ( 2 3 + ϵ) n + m , then G contains the square of a hamitonian path between any two edges, which implies the squares of a Hamiltonian cycle.

Journal ArticleDOI
TL;DR: Every graph embedded on a surface of positive genus with every face bounded by an even number of edges can be 3-colored provided all noncontractible cycles in the graph are sufficiently long.

Journal ArticleDOI
TL;DR: It is shown that a ternary matroid is representable over the rationals if and only if it can be represented over therationals by a matrix A with the property that all subdeterminants of A belong to the set {0, ±2i:i an integer}.

Journal ArticleDOI
TL;DR: This paper gives a recursive construction of ( r , s , t )-graphs for all r, s, t ≥ 2, as well as an algebraic construction of such graphs for all R, s ≥ t ≥ 3.

Journal ArticleDOI
TL;DR: B bipartite distance-regular graphs which give spin models in this way with distinct t1, ..., td are determined and it is shown that such a bipartitespecial graph satisfies a strong regularity condition (it is 2-homogeneous).

Journal ArticleDOI
TL;DR: This paper shows the existence of graphs with cn log log n edges that contain no 3-regular subgraphs and shows that graph with c k n log Δ ( G ) edges contain k -regular sub graphs.

Journal ArticleDOI
TL;DR: A short proof of Colin de Verdiere?s result that the invariant of graphs G is 3 if only if G is planar is given.

Journal ArticleDOI
TL;DR: Upper bounds on the spectral radius of graphs with n vertices and small genus are given and the relation between the spectral Radius and the genus of a graph is obtained.

Journal ArticleDOI
TL;DR: This work defines and study the chromatic, dichromatic, and Whitney number polynomials of a biased graph, which generalize those of an ordinary graph, and describes supersolvability, a matroid property which implies the characteristic polynomial has positive integral roots.

Journal ArticleDOI
TL;DR: It is shown that if such an extension is impossible, and if H is a subdivision of a simple 3-connected graph and is highly "representative", then one of two obstructions is present.

Journal ArticleDOI
TL;DR: It is shown that G arises from planar graphs by taking clique sums and subgraphs if and only if G has no K5- or V8-minor and G is monotone under taking miners andClique sums.

Journal ArticleDOI
TL;DR: How much does the edge distribution in a triangle-free graph G on n vertices deviate from the uniform edge Distribution in a typical (random) graph on n Vertices with the same number of edges?

Journal ArticleDOI
TL;DR: It is shown that every 3-connected graph embedded in the torus or the Klein bottle has a spanning planar subgraph which is 2-connected, and in fact has a slightly stronger connectivity property.

Journal ArticleDOI
TL;DR: It is shown that the independence ratio for connected 3-regular triangle-free graphs must be at least 11/30 - 2/15n, where n is the number of vertices in the graph.

Journal ArticleDOI
TL;DR: The existence of untight complete triangular embeddings is proved, the known archive of tight ones is broadened, and K30 admits a tight and an untight triangular embedding into the same surface.