Showing papers in "Electronic Notes in Discrete Mathematics in 2006"

TL;DR: This paper obtains several tight bounds on γ o ( Γ ) and Γ o ˆ (Γ ) in terms of several parameters of Γ, the minimum cardinality of a global offensive (respectively, global strong offensive) alliance in Γ.

TL;DR: This work explores the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs, where the former admits polynomial-time algorithms but the latter is NP-complete.

TL;DR: A simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O ( n 2.75 ) time, independent of the number of edges m inserted is presented.

TL;DR: An effective program for search of automata with minimal reset word of relatively great length has studied all automata of size n ≤ 10 for q = 2 (q size of alphabet) and ofsize n ≤ 7 for q ≤ 4 and there are no contradictory examples for the Cerny conjecture in this class of Automata.

TL;DR: A new unary operation called hairpin completion is defined, suggesting that a single stranded DNA molecule might produce a hairpin structure due to two biological principles, namely Watson-Crick complementarity and annealing.

TL;DR: Borders on minimum discriminating codes are provided and constructions are given and it is shown that upperbounding the size of a discriminating code is NP-complete.

TL;DR: This work analyzes the complexity of the problem of finding an hamiltonian cycle of G with the minimum number of difierent colors on special graph classes and proposes heuristic resolution algorithms for the general case.

TL;DR: In this paper, the authors prove exact results for the antibandwidth of complete k-ary trees, k even, and estimate the parameter for odd k up to the second order term.

TL;DR: A realization theorem involving different types of boundary vertex sets: extreme set, periphery, contour, and the whole boundary is presented and it is shown that the boundary is an edge-geodetic set and the contour is a monophonic set.

TL;DR: Iredundant motifs can be usefully exploited in lossy compression methods based on textual substitution and suitable for signals as well as text, and once the motifs in the authors' lossy encodings are disambiguated into corresponding lossless codebooks, they still prove capable of yielding savings over popular methods in use.

TL;DR: This work verifies an open problem of k- γ t -critical graphs and obtains some results on the characterization of total domination critical graphs of order Δ ( G ) +γ t ( G) .

TL;DR: It is shown by exhaustive computer search that the list of five known biplanes with k = 11 is complete, which implies that there exists no 3-(57, 12, 2) design, no 11211 symmetric configuration, and no (324, 57, 0, 12) strongly regular graph.

TL;DR: A new type of movement constraints for a swarm of robots in a grid environment inspired by Alex Randolphs board game Ricochet Robots are introduced.

TL;DR: The incidence game chromatic number is introduced which unifies the ideas of game Chromatic number and incidence coloring number of an undirected graph and the lower bound 3 2 ∆ is obtained for the incidence gamechromatic number of graphs of maximum degree ∆.

TL;DR: The idea is to put lower and upper bounds on the number of colors assigned to the vertices in each edge of hypergraphs to generalize the concept of the colorings of mixed hyper graphs to ‘mixed colorings’ ofhypergraphs.

TL;DR: A survey on questions about hamiltonian cycles in graphs and results about results about questions about such questions for hypergraphs are given.

TL;DR: It is shown that f ( x 1 , …, x m ) ( H , λ ) can be expressed by a polynomial in λ of degree n and as a sum of graph chromatic polynomials.

TL;DR: The aim is to find two vertex disjoint negative cycles in reasonable time which generalizes the problem of finding two vertexdisjoint odd cycles in a graph and tries to find an algorithm that acts on the graph itself, investigate structural properties of the problem and present instances where straightforward approaches fail.

TL;DR: A class of finitely parameterizable stochastic models, Quantum Predictor Models (QPMs), such that a collection of prevalent quantum statistical phenomena can be described by their means, and is identified with the induced class of discrete random processes with the class of finite-dimensional processes.

TL;DR: This work gives two characterizations of twin vertices in hypergraphs, a first one in term of clone vertices and a second one in terms of committees, and gives an algorithm to aknowledge a set as committee and two algorithms to compute clone-twin vertices classes.

TL;DR: The theory of implicit Riordan arrays which require the application of the Lagrange Inversion Formula to be dealt with are presented and several examples in which this approach gives explicit results in solving classes of combinatorial sum inversions.

TL;DR: In this article, a rough structure theorem for small separations in symmetric graphs is developed, and it is shown that whenever the diameter of G is at least 31 (k + 1 ) 2, either | A | ⩽ 2 k 3, or G has a (bounded) ring-like structure and A is efficiently contained in an interval.

TL;DR: It is shown that the k-cluster problem is solvable in polynomial time on interval graphs and two algorithms are presented, which are based on a novel matrix representation for interval graphs based on the maximal cliques in the investigated graph.

TL;DR: This talk investigates a generalized setting where there is a larger boat, having space for k items besides the rower, more items than wolf, goat, cabbage, and different forbidden pairs, and each graph G and each natural number k defines such a problem.

TL;DR: A generalization of clique family inequalities is introduced, and it is proved that several facet-defining inequalities for general claw-free graphs are of this type.

TL;DR: Cheng and Ding proved that the makespan minimization problem with arbitrary release times and identical processing rates or identical normal processing times is strongly NP-hard and the problem remains at least NP- hard even if only one job has a non-zero release time.

TL;DR: This paper provides under some conditions, a characterization of these graphs using the automorphism group of a prime amply-regular graphs, and exploits the main properties of the cartesian product, the prime factor decomposition and the notion of relatively prime graphs.