Showing papers in "Discrete Applied Mathematics in 2010"

TL;DR: The basic mathematical properties of recently introduced Zagreb coindices are explored and explicit formulae for these new graph invariants under several graph operations are presented.

TL;DR: This paper presents approximation algorithms for minimum vertex and edge guard problems for polygons with or without holes with a total of n vertices with the same approximation ratio of O(logn) times the optimal solution.

TL;DR: The lower and upper bounds on ABC index of graphs and trees are presented, and graphs for which these bounds are best possible are characterized.

TL;DR: The algorithm presents a general framework to apply dynamic programming for solving a large class of min-max problems in graphs with bounded treewidth and presents a method to transform pseudo-polynomial algorithms for the edge interdiction problem into fully polynomial approximation schemes, using a scaling and rounding technique.

TL;DR: The best upper bound for the ABC index of trees with a perfect matching is given, and the unique extremal tree is characterized, which is a molecular tree.

TL;DR: A formal mathematical framework and tools for easy design of dynamic algorithms running directly on a rank-decomposition of a graph (on contrary to the usual approach which translates aRank-Decomposition into a clique-width expression, with a possible exponential jump in the parameter).

TL;DR: The quotient of the Szeged index and the quotient Sz/Sz^* is proposed as a measure of bipartivity on a number of smaller graphs as models of networks.

TL;DR: Properties of minimal kTDS are presented and it is shown that the problem of finding k-TDSs in graphs can be translated to theProblem ofFinding k-transversals in hypergraphs and the k-tuple total domination number is investigated.

TL;DR: Improved bounds for the First Fit algorithm for the bin-packing problem are presented and it is proved C^F^F(L)@?1710C^*(L)+710 for all lists L, and the absolute performance ratio of FF is at most 127.

TL;DR: It is proved that the k-rainbow domination problem is NP-complete even when restricted to chordal graphs or bipartite graphs and a linear-time algorithm is given for theK-rainbows domination problem on trees.

TL;DR: This paper shows that the decision whether a tree allows a packing coloring with at most k classes is NP-complete, and that it is decideable in polynomial time for graphs of bounded treewidth and diameter, and fixed parameter tractable for chordal graphs.

TL;DR: The optimal values of all the 10 constraint, 500 variable instances and some of the 30 constraint, 250 variable instances of the OR-Library were found and these values were previously unknown.

TL;DR: This paper proves that unless P=NP, MinRTI cannot be approximated within a ratio of c@?lnn for some constant c>0 in polynomial time, and provides a deterministic construction of a triplet set having a similar property which is subsequently used to prove that both MaxRTC and Min RTI are NP-hard even if restricted to minimally dense instances.

TL;DR: It is proved that the matching preclusion number and the conditional matchingPreclusion number of the k-ary n-cube with even k>=4 are 2n and 4n-2, respectively.

TL;DR: This pending complexity issue is settled for all robust network optimization problems featuring polyhedral demand uncertainty, both for the single-commodity and multicommodity case, even if the corresponding deterministic versions are polynomially solvable as regular (continuous) linear programs.

TL;DR: The results settle an open question of deciding whether a (0,1)-matrix can be permuted to avoid the submatrices and imply polynomial-time recognition and isomorphism algorithms for 2-directional orthogonal ray graphs.

TL;DR: A conjecture for the maximal case based on the computer search among trees on n@?24 vertices is posed and the extremal tree that uniquely maximizes the distance spectral radius among n-vertex trees with perfect matching and fixed maximum degree @D is found.

TL;DR: In this paper, the minimum number of rows in covering arrays and radius-covering arrays has been determined precisely only in special cases, and for some parameter sets the minimum size of a covering array is determined precisely.

TL;DR: A planarity-preserving transformation is proposed that enables incorporation of vertex removals and vertex capacities in pseudo- polynomial interdiction algorithms for planar graphs and is the first pseudo-polynomial algorithm that can solve non-trivial planar flow interdictions problems with multiple sources and sinks.

TL;DR: In this paper, the average degree of the neighbor of vertex v"i is m"i=1d, and the number of common neighbors of pairs of vertices of a simple undirected graph of order n and size m is studied.

TL;DR: The forcing numbers of perfect matchings in a fullerene graph are not less than 3 by applying the 2-extendability and cyclic edge-connectivity 5 of fulleren graphs obtained recently, and Kotzig's classical result about unique perfect matching as well.

TL;DR: It is shown that treelength can be computed in time O^*(1.7549^n) by giving an exact exponential time algorithm for the Chordal Sandwich problem and showing how this algorithm can be used to compute the treelENGTH of a graph.

TL;DR: It is proved that this general algorithm makes use, for the solution of a subproblem, of an @a-approximation algorithm known for the knapsack problem and has a worst-case performance bound of 12-@a, which is always greater than @a, and therefore that this algorithm always outperforms the corresponding @ a-app approximation algorithm applied from scratch on the n+k items.

TL;DR: Algorithms are introduced that are the first algorithms for NP-hard problems whose runtimes are single exponential in the rankwidth, and show that the graphs of rankwidth at most k are exactly the graphs having an R"k-join decomposition.

TL;DR: This paper determines the radio number of the complete m-ary tree for any m>=2 with any height and construct explicitly an optimal radio labelling.

TL;DR: Using the intimate relations between random walks and electrical networks, the following effective resistance local sum rules are proved and many other local sum Rules can be deduced, including the well-known Foster's k-th formula.

TL;DR: The main result is a new characterization of this graph class: a graph GG is P6P6-free if and only if each connected induced subgraph of GG on more than one vertex contains a dominating induced cycle on six vertices or a dominating (not necessarily induced) complete bipartite subgraph.

TL;DR: This paper deals with problems on non-oriented edge-colored graphs and investigates bounded degree graphs and planar graphs, and concludes the paper with the traveling salesman problem with reload costs.

TL;DR: For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, two algorithms using only O(n) rewritable space are given that can list the minimal a-b separators and minimal vertex separators spending O(nm) time per object output.

TL;DR: This paper proves that a graph G is a block graph if and only if it satisfies two conditions: (a) The shortest path between any two vertices of G is unique; and (b) For each edge e=uv@?E(G), if x@?N"e(u) and y@? N"e (v), then, and only then, the shortest paths between x and y contains the edge e.