The Problom of Forcing Number of Perfect Matching, M.Sc. Thesis Sharif University of Technology ; Mahmoodian, Ebadollah (Supervisor) ; Ebrahimi Borogerdi, Javad (Supervisor)
Abstract
The notions of forcing edge and the forcing number of a perfect matching first appeared in 1991 by Harary, Klein and Živković. The root of these concepts can be traced to the works by Randić and Klein in 1985-1987, where the forcing number was introduced under the name of “innate degree of freedom” of a Kekulé structure, which plays an important role in the resonance theory in chemistry. Over the past three decades, more research has been done on the forcing set of perfect matchings. Here, we introduce bounds on the forcing number of perfect matching of some graphs that have already been known. Then, we extend the concept of forcing to fractional perfect matching and we introduce fractional...
Cataloging briefThe Problom of Forcing Number of Perfect Matching, M.Sc. Thesis Sharif University of Technology ; Mahmoodian, Ebadollah (Supervisor) ; Ebrahimi Borogerdi, Javad (Supervisor)
Abstract
The notions of forcing edge and the forcing number of a perfect matching first appeared in 1991 by Harary, Klein and Živković. The root of these concepts can be traced to the works by Randić and Klein in 1985-1987, where the forcing number was introduced under the name of “innate degree of freedom” of a Kekulé structure, which plays an important role in the resonance theory in chemistry. Over the past three decades, more research has been done on the forcing set of perfect matchings. Here, we introduce bounds on the forcing number of perfect matching of some graphs that have already been known. Then, we extend the concept of forcing to fractional perfect matching and we introduce fractional...
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