preliminary problems involving graph theory

... 88 (1991), 93-104 [5] M Simonovits, A method for solving extremal problems in graph theory, stability problems, in Theory of Graphs, ed by P Erd¨s and G Katona, Academic, New o York, 1968, 279-319 ... then the only graphs of order 2t that contain neither Kt nor Kt,t as a subgraph and whose number of edges equals (3) are the graphs of the form K2, ,2,4 and K2, ,2 + U where U is the graph obtained ... of edges of a graph of order 2t that contains neither Kt nor Kt,t as a subgraph equals 2t 3t − − if t is even, 2 (2) 2t − t − if t is odd (3) and equals If t is even, then the only graphs of order...

Ngày tải lên: 07/08/2014, 06:20

... extremal graph theory and Ramsey theory, or how the entirely new field of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph ... between graphs: the subgraph relation, and the ‘induced subgraph’ relation In this section we meet another: the minor relation Let e = xy be an edge of a graph G = (V, E) By G/e we denote the graph ... subject of algebraic methods in graph theory, Section 1.9 does not claim to convey an adequate impression The standard monograph here is N.L Biggs, Algebraic Graph Theory (2nd edn.), Cambridge University...

Ngày tải lên: 20/12/2013, 19:15

... separate the graph into directed subgraphs with generation vertices as its roots These subgraphs are constructed in such a way that the power can reach to all vertices in that subgraphs Figure ... 118 c) C Constructing Graph and Subgraphs D Contribution to the load o a generator f Based on the direction of the flows in all the branches of the &bus system, a directed graph can be constructed ... rooted subgraphs of Generator A, Generator B, and Generator C, respectively From these subgraphs, one can see that the power flows are supplied by respective generators Furthermore, these subgraphs...

Ngày tải lên: 03/01/2014, 19:37

... Cataloging in Publication Data Shanks Daniel Solved and unsolved problems in number theory Bibliography: p Includes index Numbers Theory of [QA241.S44 19781 5E.7 ISBN 0-8284-0297-3 I Title 77-13010 ... impression that number theory consists primarily of unsolved problems If Theorems 18 and 19 have unleashed a flood of such problems for us, they mill also lead to some beautiful theory To that we ... Artin's Conjecture Questions Concerning Cyclic Graphs Questions Concerning Cyclic Graphs Answers Concerning Cyclic Graphs Answers Concerning Cyclic Graphs Factors Generators of Mm Factors Generators...

Ngày tải lên: 15/03/2014, 16:03

Ngày tải lên: 31/03/2014, 16:18

... Graphs and vertex degrees Degree sequence Subgraphs and line graphs 2.2 Graph representations Data structures Graph isomorphism 2.3 Connectivity 2.4 Drawing graphs ... was to teach graph theory to first-year students in Computer Science and Information Science Of course, I needed to explain why graph theory is important, so I decided to place graph theory in the ... Different graphs with the same ordered degree sequence: (a) [3, 3, 2, 2, 2], and (b) [7, 5, 5, 4, 4, 4, 4, 3] Subgraphs and line graphs Another important concept of graphs is that of a subgraph A graph...

Ngày tải lên: 31/03/2014, 21:22

... spanning subgraph of G if V spans all of G, i.e if V = V G∩G subgraph G ⊆ G induced subgraph G[U ] spanning The Basics G G G Fig 1.1.3 A graph G with subgraphs G and G : G is an induced subgraph of ... extremal graph theory and Ramsey theory, or how the entirely new field of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph ... between graphs: the subgraph relation, and the ‘induced subgraph’ relation In this section we meet another: the minor relation Let e = xy be an edge of a graph G = (V, E) By G/e we denote the graph...

Ngày tải lên: 01/04/2014, 19:20

... two graphs G = (V , E ) is a subgraph of G (G ⊆ G) if V ⊆ V and E ⊆ E, i.e., the graph G contains graph G Graph G is called also a supergraph of G (G ⊇ G ) If either V ⊂ V or E ⊂ E, the graph ... of the duality, that graph G is a dual of G The graph G is called the primal graph and G the dual graph Dual graphs are denoted by a line above the big letter If a planar graph G is a dual of ... constraints Introduction Graphical models are a marriage between probability theory and graph theory [1] A graphical model is a probabilistic model defined in terms of a graph in which the nodes...

Ngày tải lên: 24/04/2014, 12:34

... Theory and Nonlinear Boundary Value Problems Chapman and hall/CRC Press, Boca Raton (2005) 10 Gasiński, L, Papageorgiou, NS: Nontrivial solutions for a class of resonant p-Laplacian Neumann problems ... this article as: Yang and Zhang: Existence results for a class of nonlocal problems involving p-Laplacian Boundary Value Problems 2011 2011:32 ... p−1 f (x, u) = m0 |u|p−2 u − |u|q−2 u, 2η Yang and Zhang Boundary Value Problems 2011, 2011:32 http://www.boundaryvalueproblems.com/content/2011/1/32 Page of hypotheses (F0), (F1), (F2) and (1.2)...

Ngày tải lên: 20/06/2014, 22:20

... Semipositone problems arise in bulking of mechanical systems, design of suspension bridges, chemical reactions, astrophysics, combustion, and management of natural resources The studies regarding problems ... created motivation for the study of problems with variable exponent Note that Mihailescu et al [20,21] were the first authors to study anisotropic elliptic problems with variable exponent Our ... associated energy functional Let us point out that, to the best of our knowledge, discrete problems like (1.1) involving anisotropic exponents have been discussed for the first time by Mihailescu,...

Ngày tải lên: 20/06/2014, 22:20

... interval graphs, graphs with forbidden subgraphs, Boolean graphs, hypercubes, and so on, graph extensions - hypergraphs, digraphs and orgraphs, labeled and weighted graphs, infinite graphs, random graphs, ... distances from graph theory perspective 5.2 Subsets approach 5.2.1 Subgraph theory In this section we make use of one of the properties in graph theory related to the design of subgraphs as presented ... = with N = 5.2.2 Supergraph theory The concept of supergraphs is totally opposite to what was introduced with the subgraphs Although this concept is not treated in graph theory because of its...

Ngày tải lên: 28/06/2014, 17:20

... EBook of Some Famous Problems of the Theory of Numbers and in particular Waring’s Problem, by G H (Godfrey Harold) Hardy *** END OF THIS PROJECT GUTENBERG EBOOK FAMOUS PROBLEMS OF THEORY OF NUMBERS ... great side of the analytic theory of numbers, the ‘multiplicative’ theory, in which the fundamental idea is that of the resolution of a number into primes In the latter theory the right weapon is ... proper weapon in the theory of primes It would be difficult for anybody to be more profoundly interested in anything than I am in the theory of primes; but it is not of this theory that I propose...

Ngày tải lên: 28/06/2014, 19:20

... spanning subgraph of G if V spans all of G, i.e if V = V G∩G subgraph G ⊆ G induced subgraph G[U ] spanning The Basics G G G Fig 1.1.3 A graph G with subgraphs G and G : G is an induced subgraph of ... extremal graph theory and Ramsey theory, or how the entirely new field of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph ... between graphs: the subgraph relation, and the ‘induced subgraph’ relation In this section we meet another: the minor relation Let e = xy be an edge of a graph G = (V, E) By G/e we denote the graph...

Ngày tải lên: 29/06/2014, 06:20

... in Graphs and other Combinatorial Structures by Ross McConnell deals with problems related to classes of intersection graphs, including interval graphs, circular-arc graphs, probe interval graphs, ... the reader with little basic knowledge of graph theory, and it introduces the reader to the concepts of interval graphs and other families of intersection graphs The lecture includes demonstrations ... references ISBN-10: 0-387-24347-X ISBN-13: 978-0387-24347-4 e-ISBN 0-387-25036-0 Graph theory Combinatorial analysis Graph theory Data processing I Golumbic, Martin Charles II Hartman, Irith Ben-Arroyo...

Ngày tải lên: 03/07/2014, 16:09

... #R18 Here we present several problems of this type, in which the selection of x is done uniformly at random, and the functions f, ρ0 , ρ1 , , ρm are linear Hence, the problems can be reformulated ... terms of the (n-dimensional) volume of the region P ∩ Hi−1 ∩ Hi+ Thus, we are led to consider problems in which the goal is to find the volumes of the regions into which a polytope is divided ... volumes of the regions into which the simplex ∆n is divided by a family of hyperplanes The specific problems described here pertain to the cube [0, 1]n and the simplex ∆n , and the answers turn out...

Ngày tải lên: 07/08/2014, 06:22

... independence of a graph J Combin Math Combin Comput., 39:157–167, 2001 [10] Reinhard Diestel Graph theory, vol 173 of Graduate Texts in Mathematics Springer, 2nd edn., 2000 http://diestel -graph- theory. com/index.html ... , AD Lemma 2.16 For each k ∈ [1, D], • G[Ak ] is a complete graph or a null graph; • G∗ [A∗ ] is a complete graph or a null graph, and all the vertices in A∗ are of type k k (1K) in the first ... the graphs in Gβ,D for D in terms of the twin graph Chartrand et al [5] characterised5 the graphs in Gβ,D for D For consistency To be more precise, Chartrand et al [5] characterised the graphs...

Ngày tải lên: 08/08/2014, 12:22

... equation (3) 2.3.2 General blocking using graph theory This approach involves a more general blocking strategy by representing major genotypes in a graphical model This representation enables ... networks A Bayesian network is a graphical representation of a set of random variables, V, which can be organised, in a directed acyclic graph (e.g [14]) (figure la) A graph is directed when for each ... In the following sections, some details of the graphical model representation are described This is not intended to be a complete description of graphical models, which is a very comprehensive...

Ngày tải lên: 09/08/2014, 18:21

... is graphical ắ ẵ ẵ is graphical ắ ẵ ẵ ẳ is graphical ẳ ẳ ẳ is graphical The last sequence corresponds to a discrete graph , and hence also our original sequence ì is graphical Indeed, the graph ... order ắẹ , then If graph of order Let í ĩ Subgraphs ẻ ẻ ẻ ẻ D EFINITION A graph is a subgraph of a graph , denoted by , if and A subgraph spans (and is a spanning subgraph of ), if every ... of is the graph on , where complements ẻ of the complete graphs are called discrete graphs In a discrete graph Clearly, all discrete graphs of order are isomorphic with each other A graph is...

Ngày tải lên: 13/08/2014, 13:21

... the connector problem In graph theoretical terms we wish to nd an optimal spanning subgraph of a weighted 2.1 Bipartite graphs and trees 22 graph Such an optimal subgraph is clearly a spanning ... 2.6 Each connected graph has a spanning tree, that is, a spanning graph that is a tree Proof Let be a minimal connected spanning subgraph, that is, a connected spanning subgraph of such that ... 2.1 Bipartite graphs and trees 19 Trees D EFINITION A graph is called acyclic, if it has no cycles An acyclic graph is also called a forest A tree is a connected acyclic graph By Theorem...

Ngày tải lên: 13/08/2014, 13:21

... Hamiltonian graphs In the connector problem we reduced the cost of a spanning graph to its minimum There are different problems, where the cost is measured by an active user of the graph For instance, ... even order with ingly this graph is It is also -regular ậà ắ ậ ậ Example 3.4 Consider the Petersen graph on the right, which appears in many places in graph theory as a counter example ... 3.5 Let be a graph of order ẳ ẵ ẵ ẵ ẳ The Claim (ii) follows from (i), since each complete graph is hamiltonian ỉ 3.2 Hamiltonian graphs Theorem 3.6 Let and , hamiltonian 35 be a graph of order...

Ngày tải lên: 13/08/2014, 13:21