On graph of order-n with the metric dimension n-3 (original) (raw)
EasyChair Preprint No 1156 On Some Classes of Problems on Graphs
The relevance to research the complexity of resolving Graph Theory problems is caused by its numerous applications. In the given paper this problem is investigated in terms of space complexity of data structures that represent analyzed graphs, orgraphs, and directed graphs. The following two non-trivial the simplest sets of problems of Graph Theory are investigated in detail. The first set consists of the problems that can be resolved by some algorithm with space complexity linear relative to the size of the data structure that represents the analyzed graphs. The second set consists of the following problems, such that the size of the solution significantly exceeds the size of the input data. To resolve the problem some algorithm that operates on space linear relative to the size of the data structure that represents the analyzed graphs can be applied. Besides, this algorithm uses some memory of the same size for sequential generation, one fragment after another, the solution of the...
On Some Classes of Problems on Graphs
2019
The relevance to research the complexity of resolving Graph Theory problems is caused by its numerous applications. In the given paper this problem is investigated in terms of space complexity of data structures that represent analyzed graphs, orgraphs, and directed graphs. The following two non-trivial the simplest sets of problems of Graph Theory are investigated in detail. The first set consists of the problems that can be resolved by some algorithm with space complexity linear relative to the size of the data structure that represents the analyzed graphs. The second set consists of the following problems, such that the size of the solution significantly exceeds the size of the input data. To resolve the problem some algorithm that operates on space linear relative to the size of the data structure that represents the analyzed graphs can be applied. Besides, this algorithm uses some memory of the same size for sequential generation, one fragment after another, the solution of the...
Journal of Graph Algorithms and Applications
Algorithmic graph theory is a classical area of research by now and has been rapidly expanding during the last three decades. In many different contexts of computer science and applications, modelling problems by graphs is a natural and canonical process. Graph-theoretic concepts and algorithms play an important role in many fields of application, e.g. in communication network design, VLSI-design, CAD, traffic optimization or network visualization.
Unsolved problems presented at the Julius Petersen Graph Theory Conference
Discrete Mathematics, 1992
The following is a list of the problems presented in connection with the meeting. We thank all contributors. Special thanks to Herbert Fleischner, who chaired the problem session and later collected the problems in writing from the participants. Problem 1 (Adrian Bondy). Path double cover Conjecture. Any k-regular graph G can be double-covered by so that each vertex is the end of exactly two paths. Editors' comment. The formulation of the problem is based paths of length k on Bondy's oral presentation at the meeting. Bondy remarked that the conjecture is true for k = 3, and that it is related to Kostochka's conjecture (Problem 15 below). Problem 2 (Nathaniel Dean). Convex hull From among all rectilinear drawings of K,, (i.e., every edge drawn as a straight-line segment) choose one D with the fewest number of crossings. The convex hull of D must be a polygon (if n > 3). Conjecture. The convex hull of D is a triangle. Problem 3 (Nathaniel Dean). Restricted Steiner tree Suppose we are given n points at fixed locations in the plane R2. (a) Find locations for k more points so as to achieve a smallest possible minimum spanning tree (MST) on the n + k points.
Combinatorial optimization: mutual relations among graph algorithms
WSEAS Transactions on Mathematics, 2008
The Theory of Graphs is a wonderful, practical discipline. Informatics has played a big part in its development, and these two fields are strongly interconnected. This can, perhaps, mainly be seen in the design of computer algorithms. On the one hand, there are many methods which can be used for solving the same problem, while on the other hand, using effective modifications of one algorithm, we can devise methods of solving various other tasks. To educate students in the area close connected with Graph Theory and Computer Science, called as Combinatorial or Discrete Optimization, it is important to make them familiar with certain algorithms in contexts to be able to get deeper into each problem and entirely understand it. In the paper we present just a few ideas that have proved successful in teaching and learning this quite young part of mathematics.
The n -ordered graphs: A new graph class
Journal of Graph Theory, 2009
For a positive integer n, we introduce the new graph class of n-ordered graphs, which generalize partial n-trees. Several characterizations are given for the finite n-ordered graphs, including one via a combinatorial game.
Three Applications of Graph Theory
Graph theory became a very important part of mathematical modeling in the 20 th century with the advent of operations research and computer science. See [1-32]. We examine three real-world problems, two of them involving searches for spanning trees, and one involving hypercubes.
Discrete Applied Mathematics, 2016
dedicated to the second workshop in the series, held in 2005 in Prague, Czech Republic; 145-2 (2005) dedicated to the first workshop, held in 2001 in Barcelona, Spain; and 54-2/3 (1994) dedicated to a workshop held in 1989 in Eugene, which in retrospect we view as workshop number zero in what has evolved to become the successful biannual GROW workshop series. This issue comprises 14 papers authored mainly, but not exclusively, by participants of the workshop. All submissions have been carefully refereed, and we thank all the referees for their hard work. True to the name of the workshop, the papers in the current special issue report on investigations in three areas of research: Graph classes, Optimization, and Width parameters. Due to the close interconnections among these areas, most of the papers fit into more than one of them. Based on their main focus, we introduce the papers in this issue in the corresponding three groups. The area of Graph Classes is represented by papers proving new structural properties of various graph classes and exploring algorithmic consequences of these properties. Bonomo, Grippo, Milanič, and Safe initiate the study of graph classes of power-bounded clique-width and give sufficient and necessary conditions for this property. Brignall, Lozin, and Stacho study bichain graphs that are a bipartite analog of split permutation graphs. They show that these graphs admit a simple geometric representation and have a universal element of quadratic order. Golovach, Heggernes, Kanté, Kratsch, and Villanger show that all minimal dominating sets of a chordal bipartite graph can be generated in incremental polynomial, hence output polynomial, time. Konagaya, Otachi, and Uehara present a polynomial-time algorithm for the subgraph isomorphism problem on several subclasses of perfect graphs. Mertzios and Zaks study a conjecture by Golumbic, Monma, and Trotter that states that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. They prove the conjecture for every graph that admits a tolerance representation with exactly one unbounded vertex. The Optimization section consists of papers that study computational complexity and algorithmic issues of various optimization problems on graphs. Corneil, Dusart, Habib, Mamcarz, and de Montgolfier consider the problem of the recognition of various kinds of orderings produced by graph searches. To this aim, they introduce a new framework in order to handle a broad variety of