Showing papers in "Discrete Applied Mathematics in 2017"

TL;DR: In this article, the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is shown to be max { ( 3 s + 2 3 ), ( n 3 ) - ( n - s 3 ) } for all n, s, n ź 3 s+ 2.

TL;DR: The Roman domination number and Italian domination number are graph labeling problems in which each vertex is labeled with either 0, 1, or 2, and the minimum possible sum of such a labeling is γ I ( G ) of a graph G.

TL;DR: First it is shown that the decision problem associated with γ d R ( G ) is NP-complete for bipartite and chordal graphs and some sharp bounds on the double Roman domination number are presented.

TL;DR: In this article, the maximum number of hyperedges in a 3-uniform hypergraph on n vertices that does not contain a Berge cycle of a given length was studied.

TL;DR: Some recent techniques for proving the Erdős–Posa property, which reveals a connection between packing and covering problems on graphs, are described and an unified presentation of the current state of the art is provided.

TL;DR: This survey aims to summarize known algorithmic and structural results on rank-width of graphs and describes whether it is possible to decompose a graph into a tree-like structure by ‘simple’ cuts.

TL;DR: For all but three classes in this family of classes defined by forbidden induced subgraphs with at most 4 vertices, either NP-completeness or polynomial-time solvability of the problem is shown or fixed-parameter tractability is proved.

TL;DR: Results on Sierpinski graphs proper are presented on their metric aspects, domination-type invariants with an emphasis on perfect codes, different colorings, and embeddings into other graphs.

TL;DR: The 2 -good-neighbor diagnosability of B S n is 8 n - 19 under the PMC model and MM ź model for n ź 5 .

TL;DR: This paper proves that for every set of $n$ points in $[0, 1]^d$ there exists an empty box of volume at least $c_d n^{-1}$, where c_d is at least of order roughly $log d$ as $d\to \infty$.

TL;DR: In this paper, it was shown that the graph decision problem is NP-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests.

TL;DR: This paper proposes an algorithm to construct two CISTs in the crossed cube, a prominent, widely studied variant of the well-known hypercube, and the existence of two CISTERs in a special Bijective Connection network based on crossed cube is discussed.

TL;DR: This paper shows that in most other cases the k-COLORING problem for (P t ,C l)-free graphs is NP-complete, and proves that there are only finitely many minimal non-k-colorable (P 6,C 4)- free graphs for any fixed k; however, the algorithms do not have the explicit lists for higher k, and thus no certifying algorithms.

TL;DR: It is shown that, on MPT graphs, the maximum weight independent set problem can be solved in polynomial time, the coloring problem is NP-complete, and the clique cover problem has a 2-approximation.

TL;DR: It is shown that the generalized 4-connectivity of the n -dimensional hypercube Q n is ( n − 1 ) , that is, for any four vertices in Q n, there exist internally disjoint trees connecting them inQ n.

TL;DR: In this article, the authors investigated various algebraic and graph theoretic properties of the distance matrix of a graph and established tight upper and lower bounds for the row sum of a k-transmission-regular graph in terms of the number of vertices of the graph.

TL;DR: Several sharp upper and lower bounds on the inverse sum indeg index are presented in terms of some graph parameters such as the order, size, radius, number of pendant vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree.

TL;DR: This paper examines a generalized h -restricted connectivity measure for n -dimensional locally twisted cube and reveals that ź h ( L T Q n ) = 2 h ( n - h ) for 0 Ż h ź n - 2 .

TL;DR: A sharp upper bound on the Wiener index of graphs in Gn,t is established and the corresponding extremal graphs are identified.

TL;DR: It is shown that, when a linear number of vertices are removed from a generalized exchanged hypercube, its surviving graph consists of a large connected component and smaller component(s) containing altogether a rather limited number of Vertices.

TL;DR: Using a SAT-solver on top of a partial previously-known solution to improve the upper bound of the packing chromatic number of the infinite square lattice from 17 to 15, demonstrating the versatility of this technology for this approach.

TL;DR: This work explores the multiplicative Zagreb indices of bipartite graphs of order n with diameter d, and sharp upper bounds are obtained for these indices of graphs in B ( n, d ) , where B is the set of all n -vertex bipartites graphs with the diameter d.

TL;DR: A new algorithm to construct Probabilistic Neutral Bits is given and this algorithm is used to improve the existing attacks for reduced rounds of both Salsa and ChaCha.

TL;DR: It is proved that optimal NIC-planar graphs with 3.6(n-2) edges have a unique embedding and can be recognized in linear time, whereas the general recognition problem of NIC- Planar graphs is NP-complete.

TL;DR: It is proved that the (adjacency) energy of any graph (bipartite or not) is a weighted sum of the traces of even powers of the adjacency matrix, and is used to find bounds for the energy in terms of subgraphs contributing to it.

TL;DR: In this article, the authors considered a special case of 0-1 knapsack in which all the item weights are equal to 1 and the item cost is assumed to be uncertain, and two robust models, namely two-stage and recoverable ones, under discrete and interval uncertainty representations, are discussed.

TL;DR: In this paper, the authors study the game of total domination in trees and show that if a tree is a forest with no isolated vertex, then the game total domination number γ tg (G ) ≤ γ ng(G ) of G is the number of vertices chosen when Dominator and Staller start the game and both players play optimally.

TL;DR: This paper obtains compositional inverses of a class of linearized binomials permuting the kernel of the trace map and gives the compositional inverse of a new class of complete mappings.

TL;DR: An O ( n ) time and space algorithm for constructing a diagonal matrix congruent to A + x I, where A is the adjacency matrix of a cograph and x ∈ R .

TL;DR: If the positive effect of letting the cranes cooperate persists when these latter jobs are present might have a critical impact, because these tasks are performed close to the landside whereas supporting the seaside crane is performed rather close toThe seaside.