0-444-51530-5, Year: 2004,
Annals of Discrete Mathematics, 57
Description
Algorithmic Graph Theory and Perfect Graphs,
first published in
1980, has become the classic introduction
to the field. This new
Annals version continues to convey the message
that intersection
graph models are a necessary and important
tool for solving real-world
problems. It remains a stepping stone from
which the reader may
embark on one of many fascinating research
trails.
The past twenty years have been an amazingly
fruitful period of
research in algorithmic graph theory and
structured families of
graphs. Especially important have been the
theory and
applications of new intersection graph models
such as
generalizations of permutation graphs and
interval graphs. These
have lead to new families of perfect graphs
and many algorithmic
results.
A new Epilogue chapter in this second edition
surveys many of the
recent results in the area. It also gives
pointers for further
study. The book has served to unify the topic
and to act as a
spring board for researchers, and especially
graduate students,
to pursue new directions of investigation.
The book is also
suitable as the text for a seminar or special
topics course in
graph theory and combinatorial mathematics.
The book covers many applications associated
with classes of
perfect graphs, including scheduling problems
and resource. The
important classes of interval graphs and
permutation graphs are
studied, as well as comparability graph and
chordal graphs.
Coloring problems on perfect graphs in polynomial
time is
especially important in scheduling applications.
This book provides a comprehensive treatment
and includes proofs
of the major results. It remains is very
timely in the
development of the field, and the unified
approach presented
should be very useful for those learning
and working in graph
theory.
Contents
Foreword 2004.
Corrections and errata.
Foreward.
Preface.
Acknowledgments.
List of Symbols.
Chapter 1. Graph Theoretic Foundations.
Chapter 2. The Design of Efficient Algorithms.
Chapter 3. Perfect Graphs.
Chapter 4. Triangulated Graphs.
Chapter 5. Comparability Graphs.
Chapter 6. Split Graphs.
Chapter 7. Permutation Graphs.
Chapter 8. Interval Graphs.
Chapter 9. Superperfect Graphs.
Chapter 10. Threshold Graphs.
Chapter 11. Not So Perfect Graphs.
Chapter 12. Perfect Gaussian Elimination.
- 2003 3
ISBN:1-59033-859-6 -
Summary:
The aim of this volume is to introduce new
topics on the areas of
difference, differential, integrodifferential
and integral
equations, evolution equations, control and
optimization theory,
dynamic system theory, queuing theory and
electromagnetism and
their applications.
Table of Contents:
Preface; Oscillation Criteria for Higher
Order Functional
Differential Equations (Ravi P. Agarwal,
Florida Institute of
Technology and Said R. Grace, Cairo University,
Egypt); Interval
Oscillation of Second-Order Half-Linear Differential
Equations (Ravi
P. Agarwal; Wan-Tong Li, Lanzhou University,
P. R. of China);
Stability Properties of Difference Scheme
for Neutral
Differential Equations (Allaberen Ashyralyev,
Fatih University,
Turkey; Haydar Akca, King Fahd University
of Petroleum and
Minerals, Saudi Arabia; F. Yenicerioglu,
Akdeniz University,
Turkey); Global Existence of Solutions of
Fuzzy
Integrodifferential Equations (K. Balachandran
and P. Prakash,
Bharathiar University, India); Existence
of Solutions of Abstract
Integrodifferential Equation of Sobolev Type
with Nonlocal
Condition (K. Balachandran; R. Sasikera,
Kongu Nadu Arts and
Science College, India); A New Characterization
of the Radon-Nikodym
Property (Abdelhamid Bourass, Bouchaib Ferrahi
and Nouddin
Saidou, Universite Mohamed V-Agdal, Morocco);
On Semilinear
Operator Equations and Applications (Yuqing
Chen, Foshan
University, P. R. of China and Yeol Je Cho);
Existence and
Nonexistence Results for Some Degenerate
Quasilinear Problems
with Indefinite Non-Linearities (Florica-Corina
St. Cirstea,
Victoria University of Technology, Australia
and Constantin P.
Niculescu, University of Craiova, Romania);
Existence for
Integral Solutions of Nonlinear Functional
Evolutions in Lp
Spaces (Ki Sik Ha); Limit Cycles of a Class
of Polynomial Systems
and its Applications (Hanying Feng, Rui Xu,
Pinghua Yang and
Zhinqiang Wang, Shijiazhuang Mechanical Engineering
College, P. R.
of China); On Eigenvalue Intervals and Eigenfunctions
for a Class
of Singular Boundary Value Problems (Zhao
Cai Hao, Li Shan Liu,
Qufu University, P. R. of China; and Yeol
Je Cho); The Truncated
Complex Moment Problem (Chunji Li, Yanbian
University, P. R. of
China); Periodic Boundary Value Problems
for Impulsive Integro-Differential
Equations in Banach Spaces (Xinzhi Liu, University
of Waterloo);
Recurrent Dimensions of Quasi-Periodic Orbits
with Frequencies
given by Weak Lioville Numbers (Koichiro
Naito, Kumamoto
University, Japan); A Generalized Hamiltonian
Model for the
Dynamics of Human Motion (C. E. M. Pearce,
University of Adelaide
and V. Ivancevic, Defense Science and Technology
Organization,
Australia); Existence and Uniqueness Theorems
of Solutions for
Nonlinear Third-Order Boundary Value Problems
(Minghe Peui, Bei
hua University, P. R. of China and Sung Kag
Chang, Yeungnam
University, Korea); On the Stability of a
Class for Nonlinear
Differential Time-Delay Control Systems in
Banach Spaces (Vu Ngoc
Phat, University of New South Wales, Australia);
On some Topics
of Fuzzy Differential Equations and Fuzzy
Optimization Problems
via a Parametric Representation of Fuzzy
Numbers (Seiji Saito,
Osaka University, Japan); Some Fractional
Differintegral
Operators and Their Applications to Differential
Equations (H. M.
Srivastava, University of Victoria, British
Columbia); Global
Analysis in a Pure-Delay-Type Lotka-Volterra
System with one
Predator and two Preys (Rui Xu); Quasilinear
Abstract Parabolic
Evolution Equations, Non Autonomous Case
(Atsushi Yagi, Osaka
University); Global Existence of Solutions
for a Class of the
Quasilinear Parabolic Systems Arising in
Population Dynamics (Yang
Wanli, Amored Force Engineering Institute,
P. R. of China); The
Exact Non-Trivial Global Solutions for 2-Dimnesional
Landau-Lifshitz
Equations (Ganshan Yang, Yunnan National
Institute, P. R. of
China and George X. Yuan, University of Queensland,
Australia);
Existence and Stability of Static Solutions
to Landau-Lifshitz
Equation for Second Approximation of the
Effective Field (Ganshan
Yang and George X. Yuan); Extremal Solutions
of Periodic Boundary
Value Problems for One-Dimensional p-Laplacian
(Fubao Zhang,
Southeast University, P. R. of China); Index.
ISBN:1-59033-866-9 -
Summary:
The aim of this volume is to introduce and
exchange recent new
topics in the areas of probability theory
and applications in
inequality theory, stochastic analysis and
applications.
Table of Contents:
Preface; Aczel’s Inequality, Superadditivity
and Horistology (Tradafir
Balan and Maria Predoi, University of Craiova,
Romania); Some
Inequalities for the Integral Mean of Holder
Continuous Functions
Defined on Disks in a Plane (N. S. Barnett,
F. C. St. Cirstea and
S. S. Dragomir, Victoria University of Technology,
Australia);
Ostrowski Type Inequalities for Functions
whose Modulus of the
Derivatives are Convex and Applications (N.
S. Barnett, P.
Cerone, S. S. Dragomir, M. R. Pinheiro and
A. Sofa, Victoria
University of Technology); Generalized Taylor’s
Formula with
Estimates of the Remainder (P. Cerone); Three-Point
Rules and
Applications for Absolutely Continuous Functions
(P. Cerone and S.
S. Dragomir); On Parallelogram Law and Bohr’s
Inequality in n-Inner
Product Spaces (Y. J. Cho; V. Culjak, University
of Zagreb,
Croatia; M. Matic, University of Split, Croatia;
J. Pecaric,
University of Zagreb); An Integral Inequality
Related to the
Ostrowski Result and Applications (S. S.
Dragomir and A. Sofo);
On Some Variants of Jensen’s Inequality
(S. S. Dragomir; Emma
Hunt, University of Adelaide); Proofs of
Wilker’s Inequalities
Involving Trigonometric Functions (Bai-Ni
Guo, Jiaozuo Institute
of Technology, P. R. of China; Wei Li, The
First Teacher College
of Luoyang, P. R. of China; Feng Qi, Jiaozuo
Institute of
Technology); Some Osrowski Type Inequalities
for Double Integrals
if Functions whose Partial Derivatives Satisfy
Certain Convexity
Properties (G. Hanna and S. S. Dragomir,
Victoria University of
Technology); On the Mappings of Conservative
Distances (Soon-Mo
Jung, Hong-Ik University, Korea); A New Analogue
Gauss’
Functional Equations and Characterizations
of Integral Mean
Values (Young-Ho Kim, Changwon National University,
Korea);
Moments Inequalities of a Random Variable
Defined over a Finite
Interval (P. Kumar, University of Northern
British Columbia); On
Norm Inequalities of Operators in Hilbert
Space (C.-S. Lin,
Bishop’s University, Canada; Y. J. Cho);
A Continuity Property
of Parametric Projections (Sizwe Mabizela,
University of Cape
Town, South Africa); Stability of Quadratic
Functional Equations
in Banach Modules (Chun-Gil Park, Chungnam
National University,
Korea); Geometric Means, Index Mappings and
Supermultiplicativity
(C. E. M. Pearce, University of Adelaide;
S. S. Dragomir; D.
Comanescu, Timisoara University, Romania);
Index
ISBN:1-59033-853-7 -
Summary:
The aim of this volume is to introduce recent
new topics in the
areas of fixed point theory, variational
inequality and
complementarity problem theory, nonlinear
ergodic theory
difference, differential and integral equations,
control and
optimization theory, dynamic system theory,
inequality theory,
stochastic analysis and probability theory,
and their
applications
Table of Contents:
Preface; A Fixed Point Theorem on Some Nonexpansive
Type Mappings
on Complete Metric Spaces (C. Adiga and Giniswamy,
University of
Mysore, India); A Topological Degree for
Pairs (Ravi P. Agarwal,
Florida Institute of Technology and Donal
O’Regan, National
University of Galway, Ireland); Acyclic Maps
on Generalized
Convex Spaces (Mircea Balaj, Oradea University,
Romania); A
Strict Convexity of the Kobayashi Distance
(Monika Budzynska and
Tadeusz Kuczumow, Instytut Matematyki, Poland);
Generic Power
Convergence of Nonlinear Operators in Banach
Spaces (Dan
Butnariu, University of Haifa, Israel; Simeon
Reich and Alexander
J. Zaslavski, Technion-Israel Institute of
Technology);
Convergence of Implicit Iterative Process
(Shih-sen Chang, Yibin
University, P. R. of China); The Limit Points
of Asymptotic Ray-Contractive
Operators (Yong-Zhuo Chen, University of
Pittsburgh); An
Approximation for the Fourier Transform of
Lebesgue Integrable
Mappings (S. S. Dragomir, Victoria University
of Technology,
Australia; Y. J. Cho; S. S. Kim, Dongeui
University, Korea); A
Perturbed Algorithm for a New Class of Strongly
Nonlinear
Variational Inclusions with Maximal ?-Monotone
Mappings (Ya-ping
Fang, Sichuan University, P. R. of China;
Yeol Je Cho; Nan-jing
Huang, Sichuan University); The Ishikawa
and Mann Iterative
Approximation for Solutions of Variational
Inclusions with F-Strongly
Accretive Type Mappings (Gu Feng, Qiqihar
University, P. R. of
China); New Classes of Probabilistic Contractions
and
Applications to Random Operators (Olga Had?ic
and Endre Pap,
University of Novi Sad, Yugoslavia); Iterative
Approximations
with Errors of Common Fixed Points for a
Couple of Asymptotically
Nonexpansive Type Mappings in Banach Spaces
(Nan-jing Huang and
Jun Li, Sichuan University); Construction
of Fixed Points of
Strictly Pseudocontractive Mappings of Browder-Petryshn
Type in
Arbitrary Banach Spaces (D. I. Igbokwe, University
of Uyo,
Nigeria); Related Fixed Point Theorems for
Set Valued Mappings on
two Metric Spaces (S. Jain and R. K. Jain,
Dr. H. S. Gour
University ,India; B. Fisher, University
of Leicester); Some
Existence Results for Vector Optimization
Problem of Banach Space
(Moon Hee Kim and Gue Myung Lee, Pukyong
National University,
Korea); Convergence and Stability and Almost
Stability of the
Ishikawa Iteration Procedures with Errors
for Quasi-Contractive
Mappings in q-Uniformly Smooth Banach Spaces
(Zeqing Liu,
Liaoning Normal University, P. R. of China;
Jeong Sheok Ume,
Changwon National University, Korea; Shin
Min Kang); Existence
Theorem and Sensitivity Analysis of Solutions
for Generalized
Parametric Nonlinear Implicit Quasi-Variational
Inequalities (Hongzhen
Nie, Liaoning College of Foreign Trade and
Economic Relations; Li
Wang, Liaoning Normal University; Shin Min
Kang); On Fixed Point
Theorems (Dejun Tan, Anshan Normal College,
P. R. of China and
Shin Min Kang); A Common Fixed Point Theorem
for Compatible
Mappings with Application to a System of
Functional Equations
Arising in Dynamic Programming (Qinhua Wu,
Huaihai Institute of
Technology, P. R. of China; Zhefu An, Liaoning
Normal University;
Yun Sun Park and Shin Min Kang, Gyeongsang
National University);
Common Fixed Point Theorems for Multi-Valued
Mappings in Menger
PM-Spaces (Fengrong Zhang, Dalian Institute
of Light Industry, P.
R. of China; Shin Min Kang and Soo Hak Shim,
Gyeongsang National
University); Iterative Solution of Nonlinear
Equation with
Accretive Operators without Continuity Assumption
in Arbitrary
Banach Spaces (Haiyun Zhou, Shijiazhuang
Mechanical Engineering
College, P. R. of China; Yeol Je Cho); Index