Author | Graver, Jack E. author |
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Title | Combinatorics with Emphasis on the Theory of Graphs [electronic resource] / by Jack E. Graver, Mark E. Watkins |
Imprint | New York, NY : Springer New York, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9914-1 |
Descript | XVI, 352 p. online resource |
I Finite Sets -- IA Conventions and Basic Notation -- IB Selections and Partitions -- IC Fundamentals of Enumeration -- ID Systems -- IE Parameters of Systems -- II Algebraic Structures on Finite Sets -- IIA Vector Spaces of Finite Sets -- IIB Ordering -- IIC Connectedness and Components -- IID The Spaces of a System -- IIE The Automorphism Groups of Systems -- III Multigraphs -- IIIA The Spaces of a Multigraph -- IIIB Biconnectedness -- IIIC Forests -- IIID Graphic Spaces -- IIIE Planar Multigraphs -- IIIF Eulerโs Formula -- IIIG Kuratowskiโs Theorem -- IV Networks -- IVA Algebraic Preliminaries -- IVB The Flow Space -- IVC Max-FlowโMin-Cut -- IVD The Flow Algorithm -- IVE The Classical Form of Max-FlowโMin-Cut -- IVF The Vertex Form of Max-FlowโMin-Cut -- IVG Doubly-Capacitated Networks and Dilworthโs Theorem -- V Matchings and Related Structures -- VA Matchings in Bipartite Graphs -- VB 1-Factors -- VC Coverings and Independent Sets in Graphs -- VD Systems with Representatives -- VE 0, 1-Matrices -- VF Enumerative Considerations -- VI Separation and Connectivity in Multigraphs -- VIA The Menger Theorem -- VIB Generalizations of the Menger Theorem -- VIC Connectivity -- VID Fragments -- VIE Tutte Connectivity and Connectivity of Subspaces -- VII Chromatic Theory of Graphs -- VIIA Basic Concepts and Critical Graphs -- VIIB Chromatic Theory of Planar Graphs -- VIIC The Imbedding Index -- VIID The Euler Characteristic and Genus of a Graph -- VIIE The Edmonds Imbedding Technique -- VIII Two Famous Problems -- VIIIA Cliques and Scatterings -- VIIIB Ramseyโs Theorem -- VIIIC The Ramsey Theorem for Graphs -- VIIID Perfect Graphs -- IX Designs -- IXA Parameters of Designs -- IXB Design-Types -- IXC t-Designs -- IXD Finite Projective Planes -- IXE Partially-Balanced Incomplete Block Designs -- IXF Partial Geometries -- X Matroid Theory -- XA Exchange Systems -- XB Matroids -- XC Rank and Closure -- XD Orthogonality and Minors -- XE Transversal Matroids -- XF Representability -- XI Enumeration Theory -- XIA Formal Power Series -- XIB Generating Functions -- XIC Pรณlya Theory -- XID Mรถbius Functions -- Index of Symbols