Showing papers in "Journal of Combinatorial Theory, Series B in 2005"

TL;DR: It is deduced that every realization of a 6-connected graph as a two-dimensional generic framework is a unique realization, based on a new inductive characterization of 3-connected graphs whose rigidity matroid is connected.

TL;DR: The main theorem of this paper is that for fixed k, there is a finite list of graphs such that a graph G has rank-width at most k if and only if no graph in the list is isomorphic to a vertex-minor of G.

TL;DR: The bound of the chromatic number of the square of any planar graph G with maximum degree Δ ≥ 8 is bounded by χ(G2) ≤ ⌊3/2 Δ⌋ + 1, and this is asymptotically an improvement on the previously best-known bound.

TL;DR: It is shown that the probability that Rn is connected is bounded away from 0 and from 1, and that each positive integer k, with high probability Rn has linearly many vertices of a given degree.

TL;DR: It is proved that each proper 3-coloring of a face of length from 8 to 11 in a connected plane graph without cycles of length without cycles from 4 to 7 can be extended to a proper 2-coloration of the whole graph.

TL;DR: For the first time, the 2-core size is shown to be asymptotically normal, in the widest possible range of the average vertex degree.

TL;DR: It is proved that every graph with maximum degree Δ and with no isolated edges has an avd-coloring with at most Δ + 300 colors, provided that Δ > 1020.

TL;DR: It is shown that the edges of every graph can be partitioned into 4 sets such that the resultant multisets give a vertex colouring of G.

TL;DR: It is proved that if α ≫ e > 0 are not too small, then every (α, e)-regular graph on n vertices contains a family of (α/2 - O(e))n edge-disjoint Hamilton cycles, and it is derived that for every constant 0 < p < 1, with high probability in the random graph G(n, p), almost all edges can be packed into edge-redundant Hamilton cycles.

TL;DR: An algorithm is developed which delivers an optimal solution in polynomial time for every fixed k in the k-vertex-connectivity augmentation problem and derives a min-max formula for the size of a smallest augmenting set in this case.

TL;DR: A sign-nonsingular matrix of order n (n + 1) whose determinant gives Πn, whose calculation is reduced to that of a Hankel matrix oforder n whose entries are large Schroder numbers is determined.

TL;DR: The current work shows that there is a clean jump for properties with speed in a middle range, and shows that when the speed of a hereditary graph property has speed greater than ncn for all c < 1, the speed is at least Bn, the nth Bell number.

TL;DR: It is shown that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8.

TL;DR: A directed analog of the local chromatic number defined by Erdos et al. provides an upper bound for the Sperner capacity of a directed graph and a special orientation of an odd cycle is found that achieves the maximum of SPerner capacity among the differently oriented versions of the cycle.

TL;DR: It is proved that for all positive γ every sufficiently large graph G with minimum degree at least (2/3+γ)|G| contains a triangulation as a spanning subgraph, whereas this need not be the case when the minimum degree is less than 2|G|/3.

TL;DR: In this article, it was shown that for a set A of vertices of a finite digraph G, there exist k disjoint A-paths if and only if |S ∩ T| + Σ⌊½|C ∩ (A ∪ S ∪ T)|⌋ ≥ k for all S, T ⊆ V(G) with S ∩ A = T ∎ A, where the respective sum is taken over the weak components C of G - (EG-(S) ∪ EG+(T)).

TL;DR: It is shown that if G has girth at least g and average degree at least d, then tw(G) = Ω(1/g+1 (d - 1)⌊(g - 1)/2⌋).

TL;DR: All such covering graphs satisfying the following two properties are classified: (1) the covering transformation group is isomorphic to the elementary abelian p-group Zp3, and (2) the group of fiber-preserving automorphisms acts 2-arc-transitively.

TL;DR: It is proved that all circular graphs Kk/d such that k/d < 4 are multiplicative, which is done using semi-lattice endomorphism in (the skeleton of) the category of graphs to prove the multiplicativity of some graphs using the known multiplier of the odd cycles.

TL;DR: This paper shows that Gallai's conjecture asserts that the edges of G can be decomposed into ⌈n/2⌉ paths is true if H can be obtained from the emptyset by a series of so-defined α-operations.

TL;DR: A family of graphs QI(n, g) that have the property that there exists a CAN if and only if there is a homomorphism to QI(_, g), which defines a generalized colouring.

TL;DR: It is obtained necessary and sufficient conditions for G to be transitive on the 2-arcs of one or both of Γ, ΓB, for certain families of imprimitive symmetric graphs.

TL;DR: It is proved that if the average degree of the graph G after deleting any radius r ≥ 2 ball is at least d ≥ 2, then its second largest eigenvalue in absolute value λ(G) is at at least 2 √d - 1(1 - c log r/r).

TL;DR: The main goal here is to show that the constant 1/(2α - 1) of Duchet and Meyniel can be improved to a larger constant, depending on α, for all α ≥ 3, and this method does not work for α = 2.

TL;DR: It is proved that a cubic 2-connected graph which has a 2-factor containing exactly 4 odd cycles has a cycle double cover.

TL;DR: It is proved that every 6k-connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs and can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively.

TL;DR: It is proved that while almost everyindependence polynomial has a nonreal root, the average independence polynomials always have all real, simple roots.

TL;DR: It is proved that there exists a decomposition of the complete graph of order n into t edge-disjoint 2-regular subgraphs of orders m1, m2,...,mt if and only if n is even and the number of cycles containing u and v differ by at most 1.

TL;DR: It is shown that every n vertex triple system with every pair of vertices lying in at least (1/2+o(1))n triples contains a copy of the Fano plane.