03603nmm a2200385 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001700139245013500156250001700291260004800308300003300356505075900389653003501148653002701183653002701210653001701237653003001254653001801284653004501302653001801347700002701365700003101392700002901423710003401452041001901486989003801505490003901543856007201582082001001654520155301664EB000722192EBX0100000000000000057527400000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894017151401 aMelnikov, O.00aExercises in Graph TheoryhElektronische Ressourcecby O. Melnikov, V. Sarvanov, R.I. Tyshkevich, V. Yemelichev, Igor E. Zverovich a1st ed. 1998 aDordrechtbSpringer Netherlandsc1998, 1998 aVIII, 356 pbonline resource0 aABC of Graph Theory -- 1.1 Graphs: Basic Notions -- 1.2 Walks, Paths, Components -- 1.3 Subgraphs and Hereditary Properties of Graphs. Reconstructibility -- 1.4 Operations on Graphs -- 1.5 Matrices Associated with Graphs -- 1.6 Automorphism Group of Graph -- Answers to Chapter 2: Trees -- 2.1 Trees: Basic Notions -- 2.2 Skeletons and Spanning Trees -- Answers to Chapter 3: Independence and Coverings -- 3.1 Independent Vertex Sets and Cliques -- 3.2 Coverings -- 3.3 Dominating Sets -- 3.4 Matchings -- 3.5 Matchings in Bipartite Graphs -- Answers to Chapter 4: Connectivity -- 4.1 Biconnected Graphs and Biconnected Components -- 4.3 Cycles and Cuts -- Answers to Chapter 5: Matroids -- 5.1 Independence Systems -- 5.2 Matroids -- 5.3 Binary Matroids aComputer science—Mathematics aElectrical Engineering aElectrical engineering aOptimization aMathematical optimization aCombinatorics aDiscrete Mathematics in Computer Science aCombinatorics1 aSarvanov, V.e[author]1 aTyshkevich, R.I.e[author]1 aYemelichev, V.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aTexts in the Mathematical Sciences uhttps://doi.org/10.1007/978-94-017-1514-0?nosfx=yxVerlag3Volltext0 a511.6 aThis book supplements the textbook of the authors" Lectures on Graph The ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord ing to the topics of graph theory: paths, cycles, components, subgraphs, re constructibility, operations on graphs, graphs and matrices, trees, independence, matchings, coverings, connectivity, matroids, planarity, Eulerian and Hamiltonian graphs, degree sequences, colorings, digraphs, hypergraphs. Each section starts with main definitions and brief theoretical discussions. They constitute a minimal background, just a reminder, for solving the exercises. the presented facts and a more extended exposition may be found in Proofs of the mentioned textbook of the authors, as well as in many other books in graph theory. Most exercises are supplied with answers and hints. In many cases complete solutions are given. At the end of the book you may find the index of terms and the glossary of notations. The "Bibliography" list refers only to the books used by the authors during the preparation of the exercisebook. Clearly, it mentions only a fraction of available books in graph theory. The invention of the authors was also driven by numerous journal articles, which are impossible to list here