A Relationship Between Thomassen's Conjecture and Bondy's Conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43924805" target="_blank" >RIV/49777513:23520/15:43924805 - isvavai.cz</a>
Result on the web
<a href="http://epubs.siam.org/doi/10.1137/130937974" target="_blank" >http://epubs.siam.org/doi/10.1137/130937974</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/130937974" target="_blank" >10.1137/130937974</a>

Result language
angličtina
Original language name
A Relationship Between Thomassen's Conjecture and Bondy's Conjecture
Original language description
A conjecture by Bondy says: there exists a constant c_0 with 0 < c_0 leq 1 such that every cyclically 4-edge-connected cubic graph H has a cycle of length at least c_0 |V(H)|. It is known that Thomassen's conjecture (every 4-connected line graph is Hamiltonian) implies Bondy's conjecture. In this paper, we show that Bondy's conjecture implies a slightly weaker version of Thomassen's conjecture: every 4-connected line graph with minimum degree at least 5 has a Hamiltonian cycle.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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