Uporaba polregularnih delovanj grup pri nekaterih odprtih problemih v algebrajski teoriji grup / Application of semiregular group actions in some open problems in algebraic graph theory
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Naziv Tittle |
Uporaba polregularnih delovanj grup pri nekaterih odprtih problemih v algebrajski teoriji grup / Application of semiregular group actions in some open problems in algebraic graph theory |
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Akronim Acronim |
J1-5433 |
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Opis Description |
(SI) Projekt je logično nadaljevanje raziskovalnega projekta J1-2055 O problemu eksistence polregularnih elementov v 2-zaprtih tranzitivnih grupah z aplikacijo v točkovno tranzitivnih grafih, ki ga financirala Javna agencija za raziskovalno dejavnost Republike Slovenije (ARRS). Raziskovalna motivacija sloni na že dolgo let odprtem problemu na področju točkovno tranzitivnih grafov oziroma tranzitivnih permutacijskih grup. Ta problem je leta 1981 postavil predlagatelj projekta (D. Marušič, On vertex symmetric digraphs, Discrete Math. 36 (1981), 69-81), ko se je vprašal, ali ima vsak točkovno tranzitiven graf polregularen avtomorfizem. Kasneje je bil problem posplošen na 2-zaprte tranzitivne permutacijske grupe (P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997), 605–615). Kljub velikemu številu raziskovalnih člankov objavljenih v zadnjih letih, ki podajajo pozitivne delne rezultate, nas pri tem problemu čaka še veliko raziskovalnega dela. Projekt bo vseboval delo na različnih aspektih tega problema in uporabi obstoja polregularnih avtomorfizmov pri reševanju drugih odprtih problemov v algebrajski teoriji grafov. (EN) This project proposal is a natural follow up of the research project J1-2055 On the problem of existence of semiregular elements in 2-closed transitive groups with application in vertex-transitive graphs funded by Slovenian Research Agency (ARRS). The motivation comes from an open problem, posed in 1981, when the project proposal leader (D. Marušič, On vertex symmetric digraphs, Discrete Math. 36 (1981), 69-81) asked if it is true that every vertex-transitive graph has a semiregular automorphism. This problem was later generalized to 2-closed transitive permutation groups (P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997), 605–615). In spite of increasing efforts (regarding this problem) resulting in a number of partial positive results in the course over the last ten years, it seems that we still have a long way to go. The proposed project will involve work on various aspects of this problem, with applications to other open problems in algebraic graph theory. |
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Vrsta projekta Project Type |
Temeljni projekt |
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Trajanje Duration |
01/08/2013 - 31/07/2016 |
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URL URL |
https://www.sicris.si/public/jqm/search_basic.aspx?lang=slv&opdescr=search&opt=2&subopt=1&code1=cmn&code2=auto&search_term=J1-5433 |
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Vodja projekta Project Leader |
dr. Dragan Marušič |
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Sodelujoče organizacije Participating organizations |
UL Pedagoška fakulteta |
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Oddelek Department |
Oddelek za matematiko IAM |