Long paths and cycles passing through specified vertices under the average degree condition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43925530" target="_blank" >RIV/49777513:23520/16:43925530 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00373-015-1573-y" target="_blank" >http://dx.doi.org/10.1007/s00373-015-1573-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00373-015-1573-y" target="_blank" >10.1007/s00373-015-1573-y</a>

Result language
angličtina
Original language name
Long paths and cycles passing through specified vertices under the average degree condition
Original language description
Let G be a k-connected graph with k GREATER-THAN OR EQUAL TO 2. We prove the following: (i) for any two distinct vertices x, z, the graph G contains an (x,z)-path of length at least the average degree of the vertices in G-{x,z} passing through any k MINUS SIGN 2 specified vertices of G; (ii) if G has n vertices and m edges, then it contains a cycle of length at least 2m/(n MINUS SIGN 1) passing through its any kMINUS SIGN 1 specified vertices. Our results generalize a theorem of Fan on the existence of long paths and a classical theorem of Erdős and Gallai on the existence of long cycles under the average degree condition.
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/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: New excellence in human resources</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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