"On stability of the hamiltonian index under contractions and closures"@en . "[C4C13A34D685]" . . . "Broersma, Hajo" . "0" . "RIV/49777513:23520/05:00000344" . . . . "534421" . "23520" . "The hamiltonian index of a graph G is the smallest integer k such that the k-th iterated line graph of G is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an A(F)-contractible subgraph F of a graph G nor the closure operation performed on G (if G is claw-free) affects the value of the hamiltonian index of a graph G."@en . . "Xiong, Liming" . . "12"^^ . "RIV/49777513:23520/05:00000344!RIV07-MSM-23520___" . . . . . "On stability of the hamiltonian index under contractions and closures" . "Stabilita hamiltonovsk\u00E9ho indexu p\u0159i kontrakc\u00EDch a uz\u00E1v\u011Brech"@cs . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "On stability of the hamiltonian index under contractions and closures"@en . . "Hamiltonovsk\u00FD index grafu G je definov\u00E1n jako nejmen\u0161\u00ED p\u0159irozen\u00E9 \u010D\u00EDslo k, pro kter\u00E9 je k-t\u00FD iterovan\u00FD hranov\u00FD graf grafu G hamiltonovsk\u00FD. V \u010Dl\u00E1nku nejprve ukazujeme, \u017Ee, s jednou v\u00FDjimkou, p\u0159id\u00E1n\u00ED hrany do grafu nem\u016F\u017Ee zv\u00FD\u0161it jeho hamiltonovsk\u00FD index. Tento v\u00FDsledek je pou\u017Eit k d\u016Fkazu toho, \u017Ee operace kontrakce A(F)-kontrahovateln\u00E9ho podgrafu F grafu G ani uz\u00E1v\u011Brov\u00E1 operace, aplikovan\u00E1 na G (pokud G je grafem bez K(1,3)), nem\u011Bn\u00ED hodnotu hamiltonovak\u00E9ho indexu grafu G."@cs . "Journal of Graph Theory" . "Ryj\u00E1\u010Dek, Zden\u011Bk" . "P(1M0545), Z(MSM4977751301)" . "0364-9024" . "1"^^ . "Stabilita hamiltonovsk\u00E9ho indexu p\u0159i kontrakc\u00EDch a uz\u00E1v\u011Brech"@cs . "3"^^ . . . "On stability of the hamiltonian index under contractions and closures" . . "The hamiltonian index of a graph G is the smallest integer k such that the k-th iterated line graph of G is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an A(F)-contractible subgraph F of a graph G nor the closure operation performed on G (if G is claw-free) affects the value of the hamiltonian index of a graph G." . . . "104" . "hamiltonian index; closure; contraction; line graph"@en . .