. . "2010-01-01+01:00"^^ . . "2012-12-31+01:00"^^ . . "Toky a cykly v grafech pomoc\u00ED zobrazen\u00ED mezi grafy" . " zero" . "Bu\u010F G=(V,E) orientovan\u00FD graf s vrcholy V a hranami E. Nenulov\u00FD Zn-tok je zobrazen\u00ED f:E->Zn{0}, kter\u00E9 v ka\u017Ed\u00E9m vrcholu spl\u0148uje Kirchhoff\u016Fv z\u00E1kon. V pades\u00E1t\u00FDch letech Tutte objevil, \u017Ee tento pojem je du\u00E1ln\u00ED k obarven\u00ED (rovinn\u00FDch) graf\u016F a t\u00EDm motivov\u00E1n vyslovil t\u0159i z\u00E1sadn\u00ED hypot\u00E9zy, kter\u00E9 navzdory mnoha pokus\u016Fm z\u016Fst\u00E1vaj\u00ED nevy\u0159e\u0161eny. C\u00EDlem navr\u017Een\u00E9ho projektu je prozkoumat tyto a p\u0159\u00EDbuzn\u00E9 hypot\u00E9zy a zejm\u00E9na prov\u011B\u0159it, zda je mo\u017Eno k jejich \u0159e\u0161en\u00ED vyu\u017E\u00EDt cyklov\u011B spojit\u00E1 zobrazen\u00ED (kter\u00E1 poprv\u00E9 zkoumali Linial, Meshulam a Tarsi, pak Jaeger, a ned\u00E1vno jejich zkoum\u00E1n\u00ED znovu podn\u00EDtil Ne\u0161et\u0159il a kol.). Jedn\u00E1 se o zobrazen\u00ED mezi mno\u017Einami hran graf\u016F, nap\u0159. z E(G) do E(H), takov\u00E1, \u017Ee vzor ka\u017Ed\u00E9ho cyklu vH je cyklus v G. Pomoc\u00ED takov\u00E9ho zobrazen\u00ED lze ze znalost\u00ED vlastnost\u00ED prostoru cykl\u016F H odvodit vlastnosti prostoru cykl\u016F G. V disertaci navrhovatele byl zkoum\u00E1n du\u00E1ln\u00ED typ zobrazen\u00ED (\u0159ezov\u011B spojit\u00E1 zobrazen\u00ED) a byly vy\u0161et\u0159eny vztahy s grafov\u00FDmi homomorfismy. Tento projekt se zam\u011B\u0159\u00ED na druhou stranu t\u00E9to duality a tak\u00E9 na jej\u00ED aplikace." . " nowhere" . "2012-03-30+02:00"^^ . . " space" . . . . "8"^^ . "8"^^ . "1. Byly dosa\u017Eeny nov\u00E9 v\u00FDsledky v aktu\u00E1ln\u00ED oblasti teorie graf\u016F. 2. Charakteristika v\u00FDsledk\u016F je adekv\u00E1tn\u00ED. 3. Projekt vedl k zapojen\u00ED skupiny student\u016F do v\u00FDzkumu. 4. V postdoktorsk\u00E9m projektu s jedin\u00FDm \u0159e\u0161itelem bylo b\u011Bhem t\u0159\u00ED let publikov\u00E1no 7 \u010Dl\u00E1nk\u016F v impaktovan\u00FDch odborn\u00FDch \u010Dasopisech a dal\u0161\u00EDch 2 \u010Dl\u00E1nky jsou v recenzn\u00EDm \u0159\u00EDzen\u00ED. 5. Nedostatky v \u010Derp\u00E1n\u00ED finan\u010Dn\u00EDch prost\u0159edk\u016F nebyly shled\u00E1ny."@cs . " cycle" . "GPP201/10/P337" . "graphs; nowhere; zero; flows; cycle; space; homomorphisms"@en . "http://www.isvav.cz/projectDetail.do?rowId=GPP201/10/P337"^^ . . . " flows" . "Flows and cycles in graphs using mappings between graphs"@en . . "0"^^ . . "graphs" . "0"^^ . . . "1"^^ . . "For a directed graph G=(V,E) (with vertices V and directed edges E) nowhere zero Zn-flow is a mapping f:E -> Zn{0} that satisfiesKichhoff's law at every vertex. Tutte discovered in 1950's that this is adual concept to that of a graph coloring and this led him to formulating three important conjectures, that remain unresolved in spite of many efforts. The goal of the proposed project is to research these and related conjectures and in particular to test, how usefully can one employcycle-continuous mappings (introduced by Linial, Meshulam and Tarsi, by Jaeger, and recently resurrected by Ne\u0161et\u0159il et al.). These are mappings between edge-sets of graphs, say from E(G) to E(H), such that the preimage of every cycle in H is a cycle in G. Such mapping can be used to transfer knowledge about cycle space of H to investigate cycle space of G. In the Ph.D. thesis of the applicant dual type of mappings (cut-continuous) was studied and its relations to graph homomorphisms were researched. This project will emphasize the other side of this duality and also it sapplications."@en . . "2014-01-27+01:00"^^ . . "New results were achieved in a topical problem of the graph theory. The characterization of the results is adequate. The project helped to create a student research group. The outputs of the three-year postdoctoral project with a single researcher contain 7 papers published in impacted journals, further 2 papers were submitted for publication. The financial rules were respected."@en . .