"RIV/49777513:23520/08:00500695!RIV09-MSM-23520___" . "Hamiltonian Cycles in the Square of a Graph"@en . "1"^^ . . "Hamiltonian Cycles in the Square of a Graph" . . . . "V Plzni" . "[C2882206628A]" . . . "Z\u00E1pado\u010Desk\u00E1 univerzita v Plzni" . . "Hamiltonian cycle; connection of the graphs; block graph; square; star."@en . "Hamiltonovsk\u00E9 kru\u017Enice v druh\u00E9 mocnin\u011B grafu"@cs . "Plze\u0148" . . "6"^^ . "2008-11-11+01:00"^^ . "The 2nd Young Researchers Conference on Applied Sciences" . "Hamiltonovsk\u00E9 kru\u017Enice v druh\u00E9 mocnin\u011B grafu"@cs . . . "We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a cut vertex and any two these vertices are at distance at least four." . . "Ekstein, Jan" . "S" . . "Hamiltonian Cycles in the Square of a Graph" . . "We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a cut vertex and any two these vertices are at distance at least four."@en . . "RIV/49777513:23520/08:00500695" . "369768" . . "1"^^ . "978-80-7043-698-1" . "Uk\u00E1\u017Eeme, \u017Ee za ur\u010Dit\u00FDch podm\u00EDnek graf vznikl\u00FD ztoto\u017En\u011Bn\u00EDm vrcholu ve dvou grafech s hamiltonovskou mocninou je rovn\u011B\u017E hamiltonovsk\u00FD. Uvedeme nutn\u00E9 a posta\u010Duj\u00EDc\u00ED podm\u00EDnky hamiltonovskosti druh\u00E9 mocniny souvisl\u00E9ho grafu takov\u00E9ho, \u017Ee ka\u017Ed\u00FD vrchol stupn\u011B alespo\u0148 t\u0159i v blokov\u00E9m grafu odpov\u00EDd\u00E1 artikulaci a ka\u017Ed\u00E9 dva takov\u00E9 vrcholy jsou ve vzd\u00E1lenosti alespo\u0148 \u010Dty\u0159i."@cs . "23520" . . . "Hamiltonian Cycles in the Square of a Graph"@en .