On weights of incluced paths and cycles in claw-free and K1,r-free graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F02%3A00070150" target="_blank" >RIV/49777513:23520/02:00070150 - isvavai.cz</a>
Alternative codes found
RIV/49777513:23520/02:00000335 RIV/49777513:23520/02:00000336
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On weights of incluced paths and cycles in claw-free and K1,r-free graphs
Original language description
Let $G$ be a $K_{1,r}$ on $n$ vertices. We prove that for any induced path or induced cycle on k$ vertices in $G(kgeq2r-1 or kgeq2r$, respectively), the degree sum of its vertices is at most $(2r-2)(n-alpha)$ where $alpha$ is the independence numberof $G$. As a corollary we obtain an upper bound on the length of a longest induced path and a longest induced cycle in a $K_{1,r}$-free graph. Stronger bounds are given in the special case of claw-free graphs (i.e., $r=3$). Sharpness examples are also presented.
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/LN00A056" target="_blank" >LN00A056: Institute of Theoretical Computer Science (Center of Young Science)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2002
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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