"2014-12-31+01:00"^^ . "V projektu se budeme zab\u00FDvat dv\u011Bma d\u016Fle\u017Eit\u00FDmi probl\u00E9my teorie graf\u016F: (i) duhov\u00E9 barven\u00ED graf\u016F, zejm\u00E9na ur\u010Den\u00ED (\u010Di odhady) duhov\u00E9ho \u010D\u00EDsla souvislosti rc(G) dan\u00E9ho grafu G \u2013 probl\u00E9m m\u00E1 aplikace pro bezpe\u010Dn\u00FD p\u0159enos informac\u00ED mezi agenturami v komunika\u010Dn\u00EDch s\u00EDt\u00EDch; (ii) nalezen\u00ED (\u010Di odhady velikosti) nejv\u011Bt\u0161\u00EDho podgrafu dan\u00FDch vlastnost\u00ED \u2013 kru\u017Enice, cesty, trestle (2-souvisl\u00E9ho faktoru s omezen\u00FDm maxim\u00E1ln\u00EDm stupn\u011Bm) atd. v dan\u00E9m (kone\u010Dn\u00E9m) grafu \u2013 znalost t\u011Bchto podgraf\u016F m\u00E1 v\u00FDznamnou roli pro strukturu dan\u00E9ho grafu a jeho dal\u0161\u00ED grafov\u00E9 vlastnosti." . . . "edge colouring, rainbow connection, longest cycle, hamiltonicity, trestle"@en . . "1"^^ . "edge colouring" . "2013-03-18+01:00"^^ . "Duhov\u00E1 souvislost a cykly v grafech" . "0"^^ . "0"^^ . . . "0"^^ . "http://www.isvav.cz/projectDetail.do?rowId=7AMB13DE003"^^ . . "2014-06-12+02:00"^^ . . . " hamiltonicity" . . . . " rainbow connection" . "In the project, we will consider two important problems in the field of Graph Theory: (i) rainbow colouring of graphs, especially computation of (or at least bounds for) the rainbow connection number rc(G) of a given graph G \u2013 the problem has an interesting application for the secure transfer of classified information between agencies in communication networks; (ii) computation of (or at least bounds for the size of) a largest subgraph with prescribed properties \u2013 cycle, path, trestle (a spanning 2-connected subgraph of bounded degree) etc. \u2013 knowledge about such subgraphs has major importance on the structure of a given graph and its other graph properties."@en . "2013-01-01+01:00"^^ . . "7AMB13DE003" . . . "Rainbow connection and cycles in graphs"@en . . "0"^^ . . " longest cycle" . .