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Igre, porojene iz grafovske dominacije : doktorska disertacijaKošmrlj, GašperV delu preučujemo igre na grafih, ki temeljijo na dominaciji. Največ pozornosti posvetimo dominacijski igri, v kateri igralca dominator in zavlačevalka izmenično izbirata vozlišča končnega grafa, ... dokler izbrana vozlišča ne tvorijo dominacijske množice. Kot je jasno že iz imen igralcev, je dominatorjev cilj čim hitreje zaključiti igro, medtem ko zavlačevalka stremi k čim daljši igri. Igralno dominacijsko število grafa je invarianta, ki nam pove, koliko potez je potrebnih, ko oba igrata optimalno. Potem ko v prvem poglavju predstavimo zgodovino grafovske dominacije ter prve rezultate v povezavi z dominacijsko igro, se v drugem poglavju ukvarjamo z dominacijsko igro na disjunktni uniji grafov, v tretjem pa z igralnim dominacijskim številom na enostavnih družinah grafov. Četrto poglavje posvetimo realizacijam parov igralnega dominacijskega števila z visoko povezanimi družinami grafov, medtem ko v petem skonstruiramo neskončne razrede grafov, ki imajo igralno dominacijsko število (domnevno) maksimalno možno. V šestem poglavju rešimo klasični problem grafovskih invariant, in sicer, kako se invarianta poljubnega grafa spremeni, če mu odvzamemo eno povezavo ali eno vozlišče. V zadnjem poglavju nas zanimajo kombinatorne igre. Podrobneje si pogledamo kombinatorno različico dominacijske igre dom, za katero določimo Sprague-Grundyjeve vrednosti nekaterih enostavnih družin grafov.Type of material - dissertation ; adult, seriousPublication and manufacture - Ljubljana : [G. Košmrlj], 2015Language - slovenianCOBISS.SI-ID - 17209177
Link(s):
http://www.matknjiz.si/doktorati/2015/Kosmrlj-14521-12.pdf
Repository of the University of Ljubljana – RUL
Digitalna knjižnica Slovenije - dLib.siDostop z namenskih računalnikov v prostorih NUK
Author
Košmrlj, Gašper
Other authors
Klavžar, Sandi |
Konvalinka, Matjaž
Topics
grafovska dominacija |
dominacijska igra |
igralno dominacijsko število |
igre na grafih |
graph domination |
domination game |
game domination number |
games on graphs
Library/institution |
City | Acronym | For loan | Other holdings |
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FMF and IMFM, Mathematical Library, Ljubljana | Ljubljana | MAKLJ |
reading room 1 cop.
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National and University Library, Ljubljana | Ljubljana | NUK |
reading room 1 cop.
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not for loan 1 cop.
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Shelf entry
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DRS, in which the journal is indexed
Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Košmrlj, Gašper | 34750 |
Klavžar, Sandi | 05949 |
Konvalinka, Matjaž | 22401 |
Source: Personal bibliographies
and: SICRIS
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