Tolerance Graphs

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Cambridge University Press, Feb 12, 2004 - Mathematics - 265 pages
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The study of algorithmic graph theory and structured families of graphs is an important branch of discrete mathematics. It finds numerous applications, from data transmission through networks to efficiently scheduling aircraft and crews, as well as contributing to breakthroughs in genetic analysis and studies of the brain. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. One of these is the study of tolerance graphs and tolerance orders. This book contains the first thorough study of tolerance graphs and related topics, indeed the authors have included proofs of major results previously unpublished in book form. It will act as a springboard for researchers, and especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory.
 

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Contents

definitions and examples
5
Ordered sets
13
Early work on tolerance graphs
29
Trees cotrees and bipartite graphs
53
Interval probe graphs and sandwich problems
63
Bitolerance and the ordered sets perspective
84
Unit and 50 tolerance orders
98
Comparability invariance results
109
Recognition of bounded bitolerance orders
124
Algorithms on tolerance graphs
135
The hierarchy of classes of bounded bitolerance orders
146
Tolerance models of paths and subtrees of a tree
164
Directed tolerance graphs
219
Open questions and further directions of research
249
Index of symbols
260
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