Showing papers in "European Journal of Combinatorics in 2017"

TL;DR: In this article, the odd writhe, parity bracket, affine index polynomial, and arrow polynomials are defined for both classical and virtual knotoids in analogy to corresponding invariants of virtual knots.

TL;DR: This review article will describe some dramatic recent developments in the theory of bootstrap percolation (and, more generally, of monotone cellular automata with random initial conditions), and discuss some potential extensions of these methods and results to other automata.

TL;DR: DP-coloring is a generalization of list coloring introduced recently by Dvořak and Postle (2015) and it is proved that for every n -vertex graph G whose chromatic number χ is “close” to n, the DP-chromatic number of G equals χ ( G ).

TL;DR: In this paper, the authors improved upon the known upper bounds for generalised colouring numbers for graphs excluding a fixed minor, from the exponential bounds of Grohe et al. to a linear bound for the r -colouring number col r and a polynomial bound for wcol r.

TL;DR: It is proved that the automorphism group of the main supergraphs and cyclic graphs can be written as a combination of Cartesian and wreath products of some symmetric groups.

TL;DR: It is proved that every bipartite graph $G$ which is not an odd length path satisfies $\chi_{\rm irr}'(G)\leq 10$, which is the first general constant upper bound on the irregular chromatic index of bipartites graphs.

TL;DR: An asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence $\boldsymbol{d}=(d_1,\ldots, d_n)$, provided that the number of edges is at least $n + \textstyle{\frac{1}{2}} d_{\max}^4$, where $d_{\ max}$ is the maximum degree.

TL;DR: In this article, it was shown that all 3-colourings of a connected cubic graph G are not Kempe equivalent unless G is the complete graph K4 or the triangular prism.

TL;DR: It is shown that the theory of graph limits induces a meaningful notion of convergence and a corresponding version of the Szemeredi regularity lemma, and applies these results to Gibbs measures induced by sparse random factor graphs and verify the “replica symmetric solution” predicted in the physics literature under the assumption of non-reconstruction.

TL;DR: It is proved that every triangle-free planar graph admits an ( F, F 5 ) -partition, and it is shown that if for some integer d there exists a Triangle-free Planar graph that does not admit an (F, F d ) -Partition, then it is an NP-complete problem to decide whether a triangle-based graph admits such a partition.

TL;DR: The results make ample use of a symmetric commutative association scheme arising from the Gelfand pair ( S 2 n , S 2 ≀ S n ) and give an exposition of a few new interesting objects that live in this scheme as they pertain to the results.

TL;DR: It is shown that, given r ≥ 5 and n large, the balanced complete bipartite graph K n ∵ 2 , n ∕ 2 is the n -vertex graph that admits the largest number of r -edge-colorings for which there is no triangle whose edges are assigned three distinct colors.

TL;DR: It is proved that any digraph whose underlying (multi-)graph is 3 -edge-connected admits aNL-3-flow, and even a NL-2-flow in case the underlying graph is 4 -edge connected, and conjecture that 3-edge-connectivity already guarantees the existence of a NL, which, if true, would imply the 2-Color-Conjecture for planar graphs due to Victor Neumann-Lara.

TL;DR: This paper generalizes MacMahon’s classical theorem by q -enumerating lozenge tilings of a new family of hexagons with four adjacent triangles removed from their boundary.

TL;DR: It is proved that every ( 0, m f − ( m − 1 ) r ) -digraph has a ( 0 , f ) -factorization r -orthogonal to every H i ( i = 1, 2, …, k ).

TL;DR: It is shown that if a word has a 2-error overlap then it is bad, and the structures of all bad words are characterized.

TL;DR: It is proved that for any multigraph G = ( V, E ) , the number of totally cyclic orientations of G is equal to the value of P ( H G, − 1 ) where P (H G, λ ) is the chromatic polynomial of a hypergraph H G which is constructed from G.

TL;DR: An efficient way to form generating functions to compute values of parking distributions on trees and establish the positivity and log-concavity of a related polynomial is given.

TL;DR: A sharp threshold is determined for both two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph ${\mathcal G}(n,p)$.

TL;DR: A classification is given of connected half-arc-regular bi-circulants of valency 6 and the first known infinite family of half- Arc-transitive bi- Circulant of Valency 6 is constructed.

TL;DR: In this paper, the authors define and count families of subsets and supersets of planar Eulerian orientations, indexed by an integer k, that converge to the set of all planar eulerian maps with n edges as k increases.

TL;DR: An analogue of this theorem for permutations is proved and the methods used in the proof are applied to give an example of a finitely approximable permutation parameter that is not finitely forcible.

TL;DR: As a consequence of the generalization of Chen’s theorem, new families of graphs are got whose chromatic number equals their circular Chromatic number and that satisfy Hedetniemi's conjecture for the circular chromatics number.

TL;DR: R k ( C n ) ⩽ ( k − 1 4 ) n + o ( n ) is shown, obtaining the first improvement to the coefficient of the linear term by an absolute constant.

TL;DR: It is proved that every 2-connected loopless Eulerian odd- K 4 -minor-free graph with an even number of edges has an even-cycle decomposition.

TL;DR: The classical k -scribability problem proposed by Steiner and generalized by Schulte, which asks about the existence of d -polytopes that cannot be realized with all k -faces tangent to a sphere is answered.

TL;DR: It is proved that, for graphs with girth at least l − 1, statement (i) holds for every m ≥ 1 ; and it is observed that, statements (ii) and (i) also holds forevery m ≤ 1.

TL;DR: The Bouwer graphs are generalized to obtain a much larger family of vertex- and edge-transitive graphs, containing almost all so-called tightly attached quartic half-arc- transitive graphs.

TL;DR: It is proved that | G | has a Hamiltonian curve if and only if every finite vertex set of G is contained in a cycle of G .

TL;DR: In this article, it was shown that there is no homotopy invariant of Hom (T, G ) which gives an upper bound for the chromatic number of a non-bipartite graph.