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Electronic reading-room
Korcsok, Peter ; Holan, Tomáš (advisor) ; Horký, Vojtěch (referee)
Title: Electronic reading-room Author: Peter Korcsok Department: Department of Software and Computer Science Education Supervisor: RNDr. Tomáš Holan, Ph.D. Abstract: We have created an Internet application that allows registered users to share information about scientific articles. Data necessary for standard bibli- ographic record are stored for each article; any files with the text of the article in PDF or PostScript format are saved directly on the server. Articles can be sorted into categories arranged in a treelike structure. Users may rate the artic- les using marks and commentaries and discuss them. The application provides a comfortable search in stored articles; user is able to save the search parameters for future use. Addition of new article can be done using a web form or by sending an e-mail message containing all necessary data in the correct format to address of the application. Some users are selected as administrators who manage ac- counts, categories and other application settings. The work is designed in PHP and uses MySQL database. Keywords: articles, web, database
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Minimal counterexamples to flow conjectures
Korcsok, Peter ; Šámal, Robert (advisor) ; Goodall, Andrew (referee)
We say that a~graph admits a~nowhere-zero k-flow if we can assign a~direction and a~positive integer (<k) as a~flow to each edge so that total in-flow into $v$ and total out-flow from $v$ are equal for each vertex $v$. In 1954, Tutte conjectured that every bridgeless graph admits a~nowhere-zero 5-flow and the conjecture is still open. Kochol in his recent papers introduces a~computational method how to prove that a~minimal counterexample cannot contain short circuits (up to length 10). In this Thesis, we provide a~comprehensive view on this method. Moreover, since Kochol does not share his implementation and in order to independently verify the method, we provide our source code that validates Kochol's results and extend them: we prove that any minimal counterexample to the conjecture does not contain any circuit of length less than 12. Powered by TCPDF (www.tcpdf.org)
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Minimal counterexamples to flow conjectures
Korcsok, Peter ; Šámal, Robert (advisor) ; Goodall, Andrew (referee)
We say that a~graph admits a~nowhere-zero k-flow if we can assign a~direction and a~positive integer (<k) as a~flow to each edge so that total in-flow into $v$ and total out-flow from $v$ are equal for each vertex $v$. In 1954, Tutte conjectured that every bridgeless graph admits a~nowhere-zero 5-flow and the conjecture is still open. Kochol in his recent papers introduces a~computational method how to prove that a~minimal counterexample cannot contain short circuits (up to length 10). In this Thesis, we provide a~comprehensive view on this method. Moreover, since Kochol does not share his implementation and in order to independently verify the method, we provide our source code that validates Kochol's results and extend them: we prove that any minimal counterexample to the conjecture does not contain any circuit of length less than 12. Powered by TCPDF (www.tcpdf.org)
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Electronic reading-room
Korcsok, Peter ; Holan, Tomáš (advisor) ; Horký, Vojtěch (referee)
Title: Electronic reading-room Author: Peter Korcsok Department: Department of Software and Computer Science Education Supervisor: RNDr. Tomáš Holan, Ph.D. Abstract: We have created an Internet application that allows registered users to share information about scientific articles. Data necessary for standard bibli- ographic record are stored for each article; any files with the text of the article in PDF or PostScript format are saved directly on the server. Articles can be sorted into categories arranged in a treelike structure. Users may rate the artic- les using marks and commentaries and discuss them. The application provides a comfortable search in stored articles; user is able to save the search parameters for future use. Addition of new article can be done using a web form or by sending an e-mail message containing all necessary data in the correct format to address of the application. Some users are selected as administrators who manage ac- counts, categories and other application settings. The work is designed in PHP and uses MySQL database. Keywords: articles, web, database
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