Showing papers in "Journal of Combinatorial Theory, Series B in 2006"

TL;DR: It is shown that if a sequence of dense graphs G has the property that for every fixed graph F, the density of copies of F in G"n tends to a limit, then there is a natural ''limit object,'' namely a symmetric measurable function W:[0,1]^2->[0, 1].

TL;DR: A polynomial-time algorithm to approximate the branch-width of certain symmetric sub-modular functions, and gives two applications to graph "clique-width" and the area of matroid branch- width.

TL;DR: It is shown that the Bergman fan B˜(Kn) of the graphical matroid of the complete graph Kn is homeomorphic to the space of phylogenetic trees Tn × R, which leads to a proof that the link of the origin in Tn is homeomorphism to the order complex of the proper part of the partition lattice Πn.

TL;DR: It is proved that, under a mild hypothesis on the form of this equation, these k + 1 series are algebraic, and a strategy to compute a polynomial equation for each of them is given, which generalizes the so-called kernel method and quadratic method.

TL;DR: Every 3-uniform hypergraph on n vertices whose minimum degree is at least n/[email protected] contains a Hamilton cycle.

TL;DR: It is proved that the maximum number of edges in an n -vertex r -uniform hypergraph containing no copy of H l + 1 ( r ) is ( l ) r l r n r + o ( n r ) as n → ∞ .

TL;DR: It is proved that forevery proper minor-closed class I of graphs there exists a constant c such that for every integer n the class I includes at most n!cn graphs with vertex-set.

TL;DR: Improving a result of Erdos, Gyarfas and Pyber for large n, it is shown that for every integer r>=2 there exists a constant n"0=n"0(r) such that if n>=n"-0 and the edges of the complete graph K"n are colored with r colors then the vertex set of K" n can be partitioned into at most 100rlogr vertex disjoint monochromatic cycles.

TL;DR: It is proved here that it is NP-hard to determine the crossing number of a simple 3-connected cubic graph, which implies that the minor-monotone version of the crossingNumber problem is also NP- hard, which has been open till now.

TL;DR: It is proved that if M is a family of matroids described by a sentence in the monadic second-order logic of matroid logic, then there is a finite tree automaton accepting exactly those parse trees which build vector representations of the bounded-branch-width representable members of M.

TL;DR: An enumeration formula is derived for the number Θγ (e) of unrooted maps on an orientable surface Sγ of a given genus γ and with a given number of edges e that can be calculated whenever the numbers Ng (f) are known for g and f ≤ e.

TL;DR: It is shown that if n ≥ 3, then the automorphism group of the transposition graph Tra(T) is isomorphic to Aut( Sn, T) = {α ∈ Aut(Sn)|Tα = T} and if T is a minimal generating set of Sn then the Automorphism Group of the Cayley graph Cay(Sn, T), where R(Sn) is the right regular representation of Sn.

TL;DR: It is proved that every (simple) graph on n>=9 vertices and at least 7n-27 edges either has a K"9 minor, or is isomorphic to K"2","2"," 2","3","3,''3, or has been obtained from disjoint copies of K"1","2", by identifying cliques of size six.

TL;DR: This study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation.

TL;DR: This work lets F(k) be the maximum over all k-majority tournaments T of the size of a minimum dominating set of T, and shows that F (k) exists for all k > 0, that F(2) = 3 and that in general C1k/log k ≤ F( k) ≤ C2k log k for suitable positive constants C1 and C2.

TL;DR: This work determines when the topological spaces |G| naturally associated with a graph G and its ends are metrizable or compact and gives two proofs, one of them based on Stone's theorem that metric spaces are paracompact.

TL;DR: In this article, it was shown that the existence of integral flow polynomial that counts nowhere-zero k-flows on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes.

TL;DR: It is proved that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3/8n.

TL;DR: It is proved that if G is a @C-labelled graph and [email protected]?

TL;DR: This work shows that a bipartite graph is chordal bipartites if and only if the complement is the intersection graph of a family of pairwise compatible claws in a weighted hypercircle.

TL;DR: It is shown that the topological cycle space introduced recently by Diestel and Kuhn allows a verbatim generalisation of MacLane's criterion to locally finite graphs, which enables Kelmans' planarity criterion to be extended.

TL;DR: This paper studies a problem of intermediate difficulty: The problem of finding a maximum 2-matching that contains no 4-cycles, and presents a polynomial time algorithm and a min-max theorem.

TL;DR: It is proved that, for any finite field F, nets provide a qualitative characterization for branch-width in the class of F-representable matroids.

TL;DR: It is proved that every plane graph without 5- and 7-cycles and without adjacent triangles is 3-colorable.

TL;DR: In this article, the complete list of the 29 irreducible triangulations of the Klein bottle is given, and the construction of Lawrencenko and Negami's triangulation can be modified at two points.

TL;DR: It is proved that an excluded minor for the class of GF( q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor.

TL;DR: It is proved that if G1,...,Gk are pairwise edge-disjoint subgraphs of a graph G, then G has a well-balanced orientation G→ such that the inherited orientations Gi→ of Gi are well- balanced for all 1 ≤ i ≤ k.

TL;DR: The relationship between forbidden subgraphs and the existence of a matching is studied to characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching.

TL;DR: A natural topological extension of Nash-Williams' arboricity theorem for locally finite infinite graphs, in which the partitioning forests are acyclic in the stronger sense that their Freudenthal compactification-the space obtained by adding their ends-contains no homeomorphic image of S^1.

TL;DR: In this paper, the authors present an elementary proof of a theorem of Serre concerning the greatest eigenvalues of k-regular graphs, which implies a result of Winnie Li.