The book is written in English but it contains extensive
references to original articles in the international literature
and to a number of mathematical books. The second edition was
published in 2010 as a paperback (ISBN 978–1–8037–7441–0)
and as an ebook (ISBN 978–1–7814–4668–7).
the book also includes : online references a chapter containing definitions of basic mathematical terms, definitions of the mathematical terms and symbols used in the main chapters, an example chapter using mathematical diagrams, an index of mathematical symbols, an index of mathematical symbols defined in the book, an index of mathematical quantities and units, a glossary of mathematical terms, a glossary of mathematical symbols, a glossary of mathematical symbols defined in the book, a table of contents, a list of the further reading, the website references, the copyright page, the general acknowledgements and the list of contributors The Book is printed in Adobe Garamond and Caper LT Std. The ebook is accessible to people who are blind or partially sighted or are visually impaired or have a print reading device (such as a Braille printer or a talking book) or to people with dyslexia. It has been produced using the latest printing technology to ensure the best quality possible.
This is a rare book from Stanford University's
Sloan Collection.
Q:
Given an example of a graph with no perfect matching, show that the complement of an odd cycle also has no perfect matching
Question:
Let $G$ be a graph with a perfect matching. We know that the complement of $G$ has a perfect matching, but it is not possible that the complement of an odd cycle has a perfect matching. Hence, $G$ must be odd.
Proof:
Suppose to the contrary that the complement of an odd cycle has a perfect matching. We can write $ ext{CF}(G)$ for the complement of an odd cycle.
Then $ ext{CF}(G)$ has a perfect matching since it has a perfect matching in the complement. This leads us to a contradiction since $ ext{CF}(G)$ is odd.
Therefore, there can be no perfect matching in $ ext{CF}(G)$. This is a contradiction. Hence, there can be no perfect matching in $G$.
Could you please confirm whether my solution is correct?
A: 01e38acffe
Download free Physics Insights chapter summaries and chapter analysis on Math, Physics, Science, Engineering, Biology, Chemistry, Calculus, Statistics, Economics, and more. Available on PDF, ePUB, and Kindle.
physics, engineering and mathematics mathematics -...
Download free Mechanics chapter summaries and chapter analysis on Math, Physics, Engineering, Business, Medicine, Math, Science, History, Economics, Accounting, and more. Available on PDF, ePUB, and Kindle.
engineering, physics and mathematics -...
Download free Neuroscience chapter summaries and chapter analysis on Math, Neuroscience, Psychology, Neuroscience, Psychiatry, Science, Neuroscience, Cell Biology, Botany, and more. Available on PDF, ePUB, and Kindle.
neuroscience, engineering and mathematics -...
Download free Biomedical Sciences chapter summaries and chapter analysis on Math, Biomedical Sciences, Chemistry, Medicine, Microbiology, Pharmacology, Pharmacology, and more. Available on PDF, ePUB, and Kindle.
biomedical sciences, engineering and mathematics...
Download free Engineering Design chapter summaries and chapter analysis on Math, Engineering Design, Materials Science, Mechanical Engineering, Electronics Engineering, Physics, Electrical Engineering, Thermal Engineering, Civil...
engineering - engineering design chapter...
Download free Physics Insights chapter summaries and chapter analysis on Math, Physics, Science, Engineering, Business, Medicine, Math, Science, History, Economics, and more. Available on PDF, ePUB, and Kindle.
physics, engineering and mathematics -...
Download free Chemistry chapter summaries and chapter analysis on Math, Chemistry, Biochemistry, Pharmaceutical Sciences, Chemical Engineering, Medical Chemistry, Organic Chemistry, Physics, Molecular Biology,...
chemistry, engineering and mathematics -...
Download free Chemistry chapter summaries and chapter analysis on Math, Chemistry, Biochemistry, Pharmaceutical Sciences, Chemical Engineering, Medical Chemistry, Organic Chemistry, Physics, Molecular Biology,...
chemistry, engineering and mathematics -...
Download free Biophysics chapter summaries and chapter analysis on Math, Biophysics, Neuroscience, Biological Physics, Physical Biology, Physics, Biophysics, Life Science, Chemistry, Biological Chemistry,...
biophysics, engineering and mathematics -...
Download free Molecular Biology chapter summaries and chapter analysis on Math, Molecular Biology, Biochemistry, Chemical Biology, Biochemistry, Biophysics, Biological Physics, Molecular Biology,...
molecular biology,
Related links: