The study of the combinatorial properties of convex polyhedra is equivalent to the study of the properties of graphs determined by vertices and edges of convex three-dimensional polytopes. This book presents a review of both well-known and new findings on polyhedral graphs. Each chapter provides open problems and addresses an essential topic in the field. These topics include face and edge types, light edges and paths, connected subgraphs with restricted degrees of vertices, spanning subgraphs, cycles in polyhedral graphs, face-vectors and vertex-vectors of complex polyhedra, groups of symmetries, duality in polyhedra, and the coloring of polyhedral graphs.
Reihe
Sprache
Verlagsort
Verlagsgruppe
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Maße
Höhe: 234 mm
Breite: 156 mm
ISBN-13
978-1-58488-845-1 (9781584888451)
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Schweitzer Klassifikation
Pavol Jozef Safarik University, Kosice, Slovak Republic Technical University of Ilmenau, Pennewitz, Germany Pavol Jozef University, Kosice, Slovak Republic University of Central Florida, Orlando, USA Rutgers University, Piscataway, New Jersey, USA
Autor*in
Technical University of Ilmenau, Pennewitz, Germany
Reihen-Herausgeber
Introduction. Numbers of Vertices, Edges, and Faces of Polyhedral Graphs. Faces Types and Edge Types. Light Edges. Light Paths. Connected Subgraphs with Restricted Degrees of Their Vertices. Spanning Subgraphs. Cycles in Polyhedral Graphs. Face-Vectors and Vertex-Vectors of Convex Polyhedra. Groups of Symmetries of Convex Polyhedra. Duality in Polyhedra. Colouring of Polyhedral Graphs.
