Showing papers in "Discrete Mathematics in 2010"

TL;DR: Some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, translation Ovoids of orthogonal polar spaces and finite semifields.

TL;DR: The relation between the connectivity and the 3-connectivity of a graph is studied, and sharp upper and lower bounds of @k"3(G) are given for general graphs G, and two kinds of graphs which attain theupper and lower bound are constructed.

TL;DR: The total vertex irregularity strength of trees is determined by calculating the weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x.

TL;DR: The exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs is determined.

TL;DR: New families of good q-ary (q is an odd prime power) Calderbank-Shor-Steane (CSS) quantum codes derived from two distinct classical Bose-Chaudhuri-Hocquenghem codes, not necessarily self-orthogonal, are constructed.

TL;DR: This paper investigates how the use of the Regularity Lemma and the Blow-up Lemma can be avoided in certain extremal problems of dense graphs and presents another proof (and a general method) that avoids the use.

TL;DR: It is shown that the firefighter problem is NP-complete for cubic graphs and a polynomial time algorithm is described to decide if it is possible to save a given subset of the vertices of a graph with maximum degree three, provided the fire breaks out at a vertex of degree at most two.

TL;DR: It is proved that it is NP-complete to decide for a given chordal or chordal bipartite graph G and a given integer k whether G has a geodetic set of cardinality at most k.

TL;DR: In this paper, a simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is said to be H-supermagic if there exists a bijection f:V(G),E (G)->{1,2,3,...,|V (G),@?E(G);

TL;DR: In this paper, an upper bound for the largest signless Laplacian eigenvalue of a graph is given and all the extremal graphs are found and the well-known friendship graph is proved to be determined by the signlessLaPlacian spectrum.

TL;DR: An introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate behavior of the system, and some current areas of investigation that emphasize graph theoretic approaches.

TL;DR: The complete intersection property of toric ideals of bipartite graphs and oriented graphs was studied in this paper, where it was shown that these ideals are minimally generated by Grobner bases.

TL;DR: It is proved that all ~-graphs without triangles are determined by their Laplacian spectra and that all graphs, with one exception, areetermined by their signless Laplacan spectra.

TL;DR: In this paper, the authors study the properties of maximum G-Parking functions and provide a new bijection between them and the set of spanning trees of G with no broken circuit.

TL;DR: It is shown that, for any given non-spherical orientable closed surface F2, there exists an optimal 1-planar graph which can be embedded on F^2 as a triangulation, and it is proved that there does not exist any such graph for the nonorientable closed surfaces of genus at most 3.

TL;DR: It is proved that a nonincreasing list (d"1,...,d"n) of nonnegative integers is the list of degrees of a graph (with no loops or multi-edges) if and only if the sum is even and the list satisfies the following conditions.

TL;DR: It turns out that the rational primes p dividing the number, M(a, b,c), of plane partitions contained inside an arbitrary box of given sides a,b,c are precisely those for which a suitable monomial complete intersection fails to have the WLP in characteristic p.

TL;DR: It is shown that if n=p2^q, where p is odd, q is nonnegative, and 2n-1@?t@?4n-2-p-q, then the complete graph K"2"n has an interval t-coloring.

TL;DR: It is shown that the extremal chain hexagonal cacti with respect to the number of matchings and of independent sets belong to one of the considered types.

TL;DR: A widely applicable matrix method to find impossible differentials of block cipher structures whose round functions are bijective is introduced and it is expected that the matrix method developed will be useful for evaluating the security of block ciphers against impossible differential cryptanalysis.

TL;DR: This paper shows how to construct efficiently minimum d-transversals and minimum d -blockers in the special cases where G is a grid graph or a tree.

TL;DR: The topological approach has made it possible to extend to locally finite graphs many classical theorems of finite graph theory that do not extend verbatim, many of which solve problems or extend earlier work of Thomassen on infinite graphs.

TL;DR: Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, a new notion of a Hamiltonian decomposition of a uniform hyper graph is defined.

TL;DR: Small k-regular graphs of girth g where g=6,8,12 are obtained as subgraphs of minimal cages as well as some of these graphs have the smallest number of vertices known so far among the regular graphs with girthg.

TL;DR: A family of strong 3-quasi-transitive digraphs distinct from strong semicompleteDigraphs and strong semicmplete bipartite Digraphs are exhibited and provided to provide a complete characterization of strong 2-quasis-transitives.

TL;DR: It is shown that Cayley graphs Cay(S,C) which are automorphism-vertex-transitive, are in fact Cayley graph of rectangular groups, if the subsemigroup generated by C is an orthodox semigroup.

TL;DR: This paper shows that this construction implies the existence of chiral d-polytopes, for every rank d>=3, and describes a construction for chiral polytopes with preassigned regular facets.

TL;DR: analogs of the Hopf algebra of Free quasi-symmetric functions with bases labeled by colored permutations are introduced, which leads to the construction of generalized descent algebras associated with wreath products @C@?S"n and to the corresponding generalizations of quasi- SyMMetric functions.

TL;DR: Three-level secret sharing schemes arising from the vector space construction over a finite field F are presented and the key tool is the twisted cubic of PG(3,F).

TL;DR: It is shown that the duality relation satisfied by the ribbon graph polynomial can be understood in terms of knot theory and a simple proof of the relation is given which used the homflyPolynomial of a knot.