Complete graph immersions and minimum degree

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385403" target="_blank" >RIV/00216208:11320/18:10385403 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/jgt.22206" target="_blank" >https://doi.org/10.1002/jgt.22206</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22206" target="_blank" >10.1002/jgt.22206</a>

Result language
angličtina
Original language name
Complete graph immersions and minimum degree
Original language description
An immersion of a graph H in another graph G is a one-to-one mapping phi:V(H)V(G) and a collection of edge-disjoint paths in G, one for each edge of H, such that the path Puv corresponding to the edge uv has endpoints phi(u) and phi(v). The immersion is strong if the paths Puv are internally disjoint from phi(V(H)). We prove that every simple graph of minimum degree at least 11t+7 contains a strong immersion of the complete graph Kt. This improves on previously known bound of minimum degree at least 200t obtained by DeVos etal. Our result supports a conjecture of Lescure and Meyniel(also independently proposed by Abu-Khzam and Langston), which is the analogue of famous Hadwiger's conjecture for immersions and says that every graph without a Kt-immersion is (t-1)-colorable.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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