Showing papers in "Discrete Mathematics in 2009"

TL;DR: This paper offers a survey of selected recent results on total domination in graphs and defines a set S of vertices in a graph G if every vertex of G is adjacent to some vertex in S.

TL;DR: In this paper, van Dam et al. gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph and formulated some research questions on the topic.

TL;DR: Estimates suggest that almost all d-dimensional clique complexes have only one nonvanishing dimension of homology, and cannot rule out the possibility that they are homotopy equivalent to wedges of a spheres.

TL;DR: This paper surveys known results for the n-queens problem of placing n nonattacking queens on an nxn chessboard and considers extensions of the problem, e.g. other board topologies and dimensions, and investigates a number of open research areas.

TL;DR: This paper proposes a new method of using Cayley graphs for classification of data using the endomorphism monoids of graphs, a convenient tools expressing asymmetries of the graphs.

TL;DR: The intersection graph G(R) of nontrivial left ideals of a ring R is considered, and the values of n for which G(Z"n) is connected, complete, bipartite, planar or has a cycle are determined.

TL;DR: It is shown how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors, and how the sequence characterization is applied to construct easily a Riordan array.

TL;DR: An upper bound for @g"p (G) in terms of the k-colouring number col"k(G) of G for k=2^p^-^2 is proved and an alternate proof of the equivalence of (a) and (c) is given.

TL;DR: In this article, the threshold for connectivity of a uniform random intersection graph G(n,m,k) when n->~ in many situations has been determined, for example, when k is a function of n such that k>=2 and [emailprotected]?n^@[email protected]? for some fixed positive real number @a.

TL;DR: This work proves that deciding whether hn(G)@?k is NP-complete and presents polynomial-time algorithms for computing hn (G) when G is a unit interval graph, a cograph or a split graph.

TL;DR: In this article, a simple realization of a graph associahedron polytope using integer coordinates is given, given any finite graph, and a simple solution is presented.

TL;DR: The asymptotically sharp upper bound W"e(G)@?2^55^5n^5+O(n^9^/^2) for graphs of order n is proved.

TL;DR: In this paper, a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, called irreducible triangulations, was introduced.

TL;DR: This paper shows that for any connected graph G of order n>=3, @c"R(G)+@c (G)2@?n, where @c(G) is the domination number of G, and proves that the minimum and maximum values of |V"0|,|V"1|, •V"2| for a @ c"R-function f=(V" 0, V"1,V" 2) of a graph G?

TL;DR: This work considers the game of Cops and Robbers played on finite and countably infinite connected graphs, and considers the ratio of the capture time to the number of vertices, and extends this notion of capture time density to infinite graphs.

TL;DR: In this paper, the concept of weighted lattice polynomial functions (WLPFs) was introduced and defined as polynomials constructed from both variables and parameters in an arbitrary bounded distributive lattice.

TL;DR: The spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product are studied.

TL;DR: It is proved that for partially ordered sets (posets) with a least element 0, the chromatic number and the clique number coincide and the condition under which posets are not finitely colorable is given.

TL;DR: It is proved that every finite group G has a generating set of size at most log"2|G|, such that the corresponding Cayley graph contains a Hamiltonian cycle.

TL;DR: It is proved that tvs(G)@[email protected]?n/@ [email protected]?+1 for each graph of order n and with minimum degree @d>0.

TL;DR: The authors study zero-sum partitions of subsets in abelian groups, and apply the results to the study of anti-magic trees, and extension to the nonabelian case is given.

TL;DR: This paper extends Schiermeyer's result to all plausible n and hence determine the rainbow number of matchings.

TL;DR: Special classes of graphs are examined which include complete graphs, regular bipartite graphs, chains and cycles and the complexity status of finding minimum transversals and blockers in arbitrary graphs is studied.

TL;DR: It is shown that there are no perfect 2-error correcting Lee codes of block length 5 and 6 over Z, which provides additional support for the Golomb Welch conjecture as it settles the two smallest cases open so far.

TL;DR: It is proved that all lollipop graphs are determined by their Q-spectrum, that is, any graph having the same spectrum as G is isomorphic to G.

TL;DR: This work provides a characterization of radial trees as well as a geometrical interpretation of the characterization.

TL;DR: Several characterizations and recognition algorithms have been formulated for circular-arc graphs and its subclasses, with emphasis on the linear time algorithms.

TL;DR: It is proved that certain complexes on directed acyclic graphs are shellable and two theorems used for breaking and gluing such complexes are proved and applied to generalize the results by Kozlov.

TL;DR: This work presents a practical and elegant method for generating all (s,t)-combinations (binary strings with s zeros and t ones): Identify the shortest prefix ending in 010 or 011, and rotate it by one position to the right, which gives an order to (s),t-combinations that is circular and genlex.

TL;DR: The antibandwidth problem is solved precisely for two-dimensional meshes, tori and estimate the antib andwidth value for hypercubes up to the third-order term and basic facts and exact results for the same product graphs as for the antiband width are proved.