05441nam 2200733Ia 450 991013951000332120200520144314.097866138145559781118623091111862309697812822539021282253905978047061154804706115459780470394205047039420X(CKB)2550000000005876(EBL)477664(OCoLC)521028724(SSID)ssj0000338275(PQKBManifestationID)11230390(PQKBTitleCode)TC0000338275(PQKBWorkID)10297001(PQKB)11458251(MiAaPQ)EBC477664(PPN)197881440(Perlego)1008128(EXLCZ)99255000000000587620081015d2009 uy 0engur|n|---|||||txtccrGraph theory and applications with exercises and problems /Jean-Claude FournierLondon ;ISTE ;Hoboken, NJ Wiley20091 online resource (284 p.)ISTE ;v.72Description based upon print version of record.9781848210707 1848210701 Includes bibliographical references and index.Graph Theory and Applications with Exercises and Problems; Table of Contents; Introduction; Chapter 1. Basic Concepts; 1.1 The origin of the graph concept; 1.2 Definition of graphs; 1.2.1 Notation; 1.2.2 Representation; 1.2.3 Terminology; 1.2.4 Isomorphism and unlabeled graphs; 1.2.5 Planar graphs; 1.2.6 Complete graphs; 1.3 Subgraphs; 1.3.1 Customary notation; 1.4 Paths and cycles; 1.4.1 Paths; 1.4.2 Cycles; 1.4.3 Paths and cycles as graphs; 1.5 Degrees; 1.5.1 Regular graphs; 1.6 Connectedness; 1.7 Bipartite graphs; 1.7.1 Characterization; 1.8 Algorithmic aspects1.8.1 Representations of graphs inside amachine1.8.2 Weighted graphs; 1.9 Exercises; Chapter 2. Trees; 2.1 Definitions and properties; 2.1.1 First properties of trees; 2.1.2 Forests; 2.1.3 Bridges; 2.1.4 Tree characterizations; 2.2 Spanning trees; 2.2.1 An interesting illustration of trees; 2.2.2 Spanning trees in a weighted graph; 2.3 Application: minimum spanning tree problem; 2.3.1 The problem; 2.3.2 Kruskal's algorithm; 2.3.3 Justification; 2.3.4 Implementation; 2.3.5 Complexity; 2.4 Connectivity; 2.4.1 Block decomposition; 2.4.2 k-connectivity; 2.4.3 k-connected graphs2.4.4 Menger's theorem2.4.5 Edge connectivity; 2.4.6 k-edge-connected graphs; 2.4.7 Application to networks; 2.4.8 Hypercube; 2.5 Exercises; Chapter 3. Colorings; 3.1 Coloring problems; 3.2 Edge coloring; 3.2.1 Basic results; 3.3 Algorithmic aspects; 3.4 The timetabling problem; 3.4.1 Roomconstraints; 3.4.2 An example; 3.4.3 Conclusion; 3.5 Exercises; Chapter 4. Directed Graphs; 4.1 Definitions and basic concepts; 4.1.1 Notation; 4.1.2 Terminology; 4.1.3 Representation; 4.1.4 Underlying graph; 4.1.5 "Directed" concepts; 4.1.6 Indegrees and outdegrees; 4.1.7 Strongly connected components4.1.8 Representations of digraphs inside a machine4.2 Acyclic digraphs; 4.2.1 Acyclic numbering; 4.2.2 Characterization; 4.2.3 Practical aspects; 4.3 Arborescences; 4.3.1 Drawings; 4.3.2 Terminology; 4.3.3 Characterization of arborescences; 4.3.4 Subarborescences; 4.3.5 Ordered arborescences; 4.3.6 Directed forests; 4.4 Exercises; Chapter 5. Search Algorithms; 5.1 Depth-first search of an arborescence; 5.1.1 Iterative form; 5.1.2 Visits to the vertices; 5.1.3 Justification; 5.1.4 Complexity; 5.2 Optimization of a sequence of decisions; 5.2.1 The eight queens problem5.2.2 Application to game theory:finding a winning strategy5.2.3 Associated arborescence; 5.2.4 Example; 5.2.5 The minimax algorithm; 5.2.6 Implementation; 5.2.7 In concrete terms; 5.2.8 Pruning; 5.3 Depth-first search of a digraph; 5.3.1 Comments; 5.3.2 Justification; 5.3.3 Complexity; 5.3.4 Extended depth-first search; 5.3.5 Justification; 5.3.6 Complexity; 5.3.7 Application to acyclic numbering; 5.3.8 Acyclic numbering algorithms; 5.3.9 Practical implementation; 5.4 Exercises; Chapter 6. Optimal Paths; 6.1 Distances and shortest paths problems; 6.1.1 A few definitions6.1.2 Types of problemsThis book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on theISTEGraph theoryGraph theoryProblems, exercises, etcGraph theory.Graph theory511/.5SK 890rvkFournier Jean-Claude521962MiAaPQMiAaPQMiAaPQBOOK9910139510003321Graph theory and applications835212UNINA05396nam 2200349z- 450 9910583582303321202207159781501738470150173847X(CKB)5460000000023744(oapen)https://directory.doabooks.org/handle/20.500.12854/89132(Perlego)950735(oapen)doab89132(EXLCZ)99546000000002374420190426d2019 uy |engurmn|---annantxtrdacontentcrdamediacrrdacarrierThe Idea of the Labyrinth from Classical Antiquity through the Middle AgesCornell University Press20191 online resource (378 p.)Ancient and medieval labyrinths embody paradox, according to Penelope Reed Doob. Their structure allows a double perspective-the baffling, fragmented prospect confronting the maze-treader within, and the comprehensive vision available to those without. Mazes simultaneously assert order and chaos, artistry and confusion, articulated clarity and bewildering complexity, perfected pattern and hesitant process. In this handsomely illustrated book, Doob reconstructs from a variety of literary and visual sources the idea of the labyrinth from the classical period through the Middle Ages.Doob first examines several complementary traditions of the maze topos, showing how ancient historical and geographical writings generate metaphors in which the labyrinth signifies admirable complexity, while poetic texts tend to suggest that the labyrinth is a sign of moral duplicity. She then describes two common models of the labyrinth and explores their formal implications: the unicursal model, with no false turnings, found almost universally in the visual arts; and the multicursal model, with blind alleys and dead ends, characteristic of literary texts. This paradigmatic clash between the labyrinths of art and of literature becomes a key to the metaphorical potential of the maze, as Doob's examination of a vast array of materials from the classical period through the Middle Ages suggests. She concludes with linked readings of four "labyrinths of words": Virgil's Aeneid, Boethius' Consolation of Philosophy, Dante's Divine Comedy, and Chaucer's House of Fame, each of which plays with and transforms received ideas of the labyrinth as well as reflecting and responding to aspects of the texts that influenced it.Doob not only provides fresh theoretical and historical perspectives on the labyrinth tradition, but also portrays a complex medieval aesthetic that helps us to approach structurally elaborate early works. Readers in such fields as Classical literature, Medieval Studies, Renaissance Studies, comparative literature, literary theory, art history, and intellectual history will welcome this wide-ranging and illuminating book.Ancient and medieval labyrinths embody paradox, according to Penelope Reed Doob. Their structure allows a double perspective-the baffling, fragmented prospect confronting the maze-treader within, and the comprehensive vision available to those without. Mazes simultaneously assert order and chaos, artistry and confusion, articulated clarity and bewildering complexity, perfected pattern and hesitant process. In this handsomely illustrated book, Doob reconstructs from a variety of literary and visual sources the idea of the labyrinth from the classical period through the Middle Ages.Doob first examines several complementary traditions of the maze topos, showing how ancient historical and geographical writings generate metaphors in which the labyrinth signifies admirable complexity, while poetic texts tend to suggest that the labyrinth is a sign of moral duplicity. She then describes two common models of the labyrinth and explores their formal implications: the unicursal model, with no false turnings, found almost universally in the visual arts; and the multicursal model, with blind alleys and dead ends, characteristic of literary texts. This paradigmatic clash between the labyrinths of art and of literature becomes a key to the metaphorical potential of the maze, as Doob's examination of a vast array of materials from the classical period through the Middle Ages suggests. She concludes with linked readings of four "labyrinths of words": Virgil's Aeneid, Boethius' Consolation of Philosophy, Dante's Divine Comedy, and Chaucer's House of Fame, each of which plays with and transforms received ideas of the labyrinth as well as reflecting and responding to aspects of the texts that influenced it.Doob not only provides fresh theoretical and historical perspectives on the labyrinth tradition, but also portrays a complex medieval aesthetic that helps us to approach structurally elaborate early works. Readers in such fields as Classical literature, Medieval Studies, Renaissance Studies, comparative literature, literary theory, art history, and intellectual history will welcome this wide-ranging and illuminating book.Literary studies: classical, early & medievalbicsscLiterary studies: ancient, classical & medievalLiterary studies: classical, early & medievalDoob Penelope Reedauth499202BOOK9910583582303321Idea of the labyrinth737630UNINA