Table of Contents
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 Euler’s Formula.- IIIG Kuratowski’s Theorem.- IV Networks.- IVA Algebraic Preliminaries.- IVB The Flow Space.- IVC Max-Flow—Min-Cut.- IVD The Flow Algorithm.- IVE The Classical Form of Max-Flow—Min-Cut.- IVF The Vertex Form of Max-Flow—Min-Cut.- IVG Doubly-Capacitated Networks and Dilworth’s 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 Ramsey’s 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 Pólya Theory.- XID Möbius Functions.- Index of Symbols.
