About: Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy.

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About: Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy. Goto Sponge NotDistinct Permalink

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Description	Luczak and Pfender \cite{88} proved that if a graph $G$ is 3-connected and $K_{1,3}P_{11}$-free, then $G$ is hamiltonian. Moreover, Luczak et al. \cite{8} showed an example a non hamiltonian 3-connected $CP_{12}$-free graph. This result give a motivation to find an upper bound for the number $i$ such that every 3-connected $CZ_{i}$-free graph is hamiltonian. We will show that if a $G$ is 3-connected and $CZ_{6}$-free graph, then $G$ is hamiltonian. Pairs of connected graphs $X,Y$ such that a graph $G$ being 2-connected and $XY$-free implies $G$ is hamiltonian were characterized by Bedrossian. Using the closure concept for claw-free graphs, Ryj\' a\v cek simplified the characterization by showing that if considering the closure of $G$, the list in the Bedrossian's characterization can be reduced to one pair, namely, $K_{1,3},N_{1,1,1}$ (where $K_{i,j}$ is the complete bipartite graph, and $N_{i,j,k}$ is the graph obtained by identifying end vertices of three disjoint paths of l Luczak and Pfender \cite{88} proved that if a graph $G$ is 3-connected and $K_{1,3}P_{11}$-free, then $G$ is hamiltonian. Moreover, Luczak et al. \cite{8} showed an example a non hamiltonian 3-connected $CP_{12}$-free graph. This result give a motivation to find an upper bound for the number $i$ such that every 3-connected $CZ_{i}$-free graph is hamiltonian. We will show that if a $G$ is 3-connected and $CZ_{6}$-free graph, then $G$ is hamiltonian. Pairs of connected graphs $X,Y$ such that a graph $G$ being 2-connected and $XY$-free implies $G$ is hamiltonian were characterized by Bedrossian. Using the closure concept for claw-free graphs, Ryj\' a\v cek simplified the characterization by showing that if considering the closure of $G$, the list in the Bedrossian's characterization can be reduced to one pair, namely, $K_{1,3},N_{1,1,1}$ (where $K_{i,j}$ is the complete bipartite graph, and $N_{i,j,k}$ is the graph obtained by identifying end vertices of three disjoint paths of l (en)
Title	Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy. Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy. (en)
skos:prefLabel	Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy. Hamiltonovske problémy v dědičných třidách grafů charakterizované zakázanými indukovanými podgrafy. (en)
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http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Saburov, Khikmat
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
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http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/09:00501757
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Graph; induced subgraph; forbidden subgraph; line graph; hamiltonian graphs; factor (en)
http://linked.open.../riv/klicoveSlovo	factor line graph Graph forbidden subgraph hamiltonian graphs induced subgraph
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http://linked.open...iv/tvurceVysledku	Saburov, Khikmat
http://localhost/t...ganizacniJednotka	23520

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