Clique covering and degree conditions for hamiltonicity in claw-free graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F01%3A00064938" target="_blank" >RIV/49777513:23520/01:00064938 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Clique covering and degree conditions for hamiltonicity in claw-free graphs
Original language description
We prove that for any sufficiently large nonhamiltonian claw-free graph $G$ satisfying a degree condition of type $sigma_k (G)>n+k^2-4k+7$ (where $k$ is a constant), the closure of $G$ can be covered by at most $k-1$ cliques. The method is illustrated by proving that every 2-connected claw-free graph $G$ of order $ngeqslant 77$ with $delta (G) geqslant 14$ and $sigma_6 (G)>n+19$ is either hamiltonian or belongs to a family of easily described exceptions.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F97%2F0407" target="_blank" >GA201/97/0407: Global properties of locally characterized classes of graphs</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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