A MINIMUM DEGREE CONDITION FORCING COMPLETE GRAPH IMMERSION
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10283295" target="_blank" >RIV/00216208:11320/14:10283295 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00493-014-2806-z" target="_blank" >http://dx.doi.org/10.1007/s00493-014-2806-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00493-014-2806-z" target="_blank" >10.1007/s00493-014-2806-z</a>
Alternative languages
Result language
angličtina
Original language name
A MINIMUM DEGREE CONDITION FORCING COMPLETE GRAPH IMMERSION
Original language description
An immersion of a graph H into a graph G is a one-to-one mapping f: V (H) -> V (G) and a collection of edge-disjoint paths in G, one for each edge of H, such that the path P (uv) corresponding to edge uv has endpoints f(u) and f(v). The immersion is strong if the paths P (uv) are internally disjoint from f(V (H)). It is proved that for every positive integer Ht, every simple graph of minimum degree at least 200t contains a strong immersion of the complete graph K (t) . For dense graphs one can say evenmore. If the graph has order n and has 2cn (2) edges, then there is a strong immersion of the complete graph on at least c (2) n vertices in G in which each path P (uv) is of length 2. As an application of these results, we resolve a problem raised by Paul Seymour by proving that the line graph of every simple graph with average degree d has a clique minor of order at least cd (3/2), where c > 0 is an absolute constant. For small values of t, 1a parts per thousand currency signta parts p
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Combinatorica
ISSN
0209-9683
e-ISSN
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Volume of the periodical
34
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
279-298
UT code for WoS article
000338324400002
EID of the result in the Scopus database
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