Showing papers in "Discrete Mathematics in 2005"

TL;DR: It is shown that, if the number of simple permutations in a pattern restricted class of permutations is finite, the class has an algebraic generating function and is defined by a finite set of restrictions.

TL;DR: The following results are given: Let T be a tree with n vertices and k pendant vertices, where equality holds if and only if G is a regular connected bipartite graph.

TL;DR: A theoretical enumeration of rooted planar quadrangulations of minimum degree 3, and some counts obtained by a program of Brinkmann and McKay that implements the algorithm that generates classes of quartic (4-regular) planar graphs are given.

TL;DR: The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed and new conjectures concerning nest distribution functions are presented.

TL;DR: A conjectured way of expressing the Hilbert series of diagonal harmonics as a weighted sum over parking functions as well as two equivalent forms of the conjecture based on the original pair of statistics for the q,t-Catalan sequence introduced by Haglund.

TL;DR: It is shown that every Steiner set in a connected graph G must also be monophonic, and that everySteiner setIn a connected interval graph H must be geodetic.

TL;DR: This work introduces partially ordered generalized patterns (POGPs), which further generalize the generalized permutation patterns (GPs) introduced by Babson and Steingrimsson, and describes many relations between POGPs and GPs and gives general theorems about the number of permutations avoiding certain classes of POGP.

TL;DR: Some new results on (g,k;1)-CDMs are obtained, which are useful in the construction of both optical orthogonal codes and Z-cyclic whist tournaments.

TL;DR: This work proposes a more general approach for 'path properties' in graphs, focusing on the behaviour of such convexities on the Cartesian product of graphs and on the classical convexity invariants, such as the Caratheodory, Helly and Radon numbers in relation with graph invariants.

TL;DR: It is shown that except for a well-defined class of graphs, k-restricted edge cuts of a connected graph G exist for any k=<@d (G)+1, where @d(G) is the minimum degree of G and an upper bound for k- restricted edge connectivity is obtained.

TL;DR: This paper describes how to use Chebyshev polynomials to evaluate the number of spanning trees in G when G belongs to one of three different classes of graphs: (i) when G is a circulant graph with fixed jumps (substantially simplifying earlier proofs), (ii) whenG is acirculant graphs with some non-fixed jumps and when (iii) G=K"n+/-C, where K"n is the complete graph on n

TL;DR: Some of the numerous connections that the chip-firing game has with some other parts of combinatorics and with theoretical physics are surveyed.

TL;DR: Fibonacci cubes are induced subgraphs of hypercubes defined in terms of Fibonacci strings as discussed by the authors, and all these graphs are median, and several enumeration results on the number of their edges and squares are obtained.

TL;DR: This work gives a simple characterization of graphs and provides a simpler recognition algorithm for finding a maximum induced matching in a graph where equality holds.

TL;DR: Two simple sufficient conditions are given for a graphic sequence @p=(d"1,d"2,..., d"n) to be potentially K"r"+"1-graphic" and it is shown that the two sufficient conditions imply a theorem due to Rao and Li et al.

TL;DR: Shiu, Lam and Chen prove the ICC for any graph with @D=3.2 colors, where @D is the maximum degree of the graph.

TL;DR: This paper investigates the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves, and finds the cover pebbles numbers of trees and some other graphs.

TL;DR: For a graph G vertex v of G and integer r>=1, G is said to be r-EKR if no intersecting subfamily of I"v^(^r^)(G) of maximum size is a star as discussed by the authors.

TL;DR: This paper contains a survey of the A-theory of simplicial complexes and graphs, a combinatorial homotopy theory developed recently, related to prior work in matroid theory, graph theory, and work on subspace arrangements.

TL;DR: It is shown that every Latin square contains a set of entries which meets each row and column exactly once while using no symbol more than twice, and some remarks about the relation between packing and covering radii for permutations are made.

TL;DR: Graphs that contain m-restricted edge cuts are characterized in this paper if they have order at least 3m-2 and for graphs without this order restriction, it is presented two necessary and sufficient conditions to determine whether they containm- restricted edge cuts.

TL;DR: The existence of several classes of cyclotomic orthomorphisms is proved and the results to R-orthomorphisms are extended.

TL;DR: A theorem of Berge is extended, showing that any disjoint union of at least r complete graphs, each of order at least two, is r-EKR.

TL;DR: It is shown that the diameter of the Kneser graph K"n^2^n^+^k is equal to @?(n-1)/k@?+1.

TL;DR: This paper shows that every convex set of vertices in a graph is the convex hull of the collection of its contour vertices, and defines a vertex to be a contour vertex if the eccentricity of every neighbor is at most as large as that of the vertex.

TL;DR: The general properties of P-matchings are explored, but especially the cases where P is the property of being acyclic or theProperty of being disconnected, and bounds on and the complexity of the maximum cardinality and minimum cardinality are considered.

TL;DR: In this article, the authors consider bijections from G onto G, where G arises from a 2m-dimensional vector space V and if such a bijection @f and its inverse leave one of the relations from above invariant, then also also the other.

TL;DR: It is proved that for any ring R, if there exists a source y in @C(R) with y^2=0, then |R|=4 and R={0,x,y,z}, where x and z are left identity elements and yx=0=yz, that @C (R) cannot be a network for any finite or infinite ring R.

TL;DR: Bouchet's conjecture is true for 6-edge connected bidirected graphs and is proved to be true with 6 replaced by 216 for 4-connected graphs.

TL;DR: This work generalizes the notion of a PD-set of a code to that of a t-PD- set of an arbitrary permutation set and finds PD-sets for miquelian Benz planes of small order and for the ruled rational normal surface of order 3 in PG(4,3) and in PG (4,4).