Decomposing graphs into paths and trees
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368795" target="_blank" >RIV/00216208:11320/17:10368795 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.endm.2017.07.032" target="_blank" >http://dx.doi.org/10.1016/j.endm.2017.07.032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.endm.2017.07.032" target="_blank" >10.1016/j.endm.2017.07.032</a>
Alternative languages
Result language
angličtina
Original language name
Decomposing graphs into paths and trees
Original language description
In [Bensmail, J., A. Harutyunyan, T.-N. Le and S. Thomassé, Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture, arXiv preprint arXiv:1507.08208 (2015)], the authors conjecture that for a fixed tree T, the edge set of any graph G of size divisible by size of T with sufficiently high degree can be decomposed into disjoint copies of T, provided that G is sufficiently highly connected in terms of maximal degree of T. In [Bensmail, J., A. Harutyunyan, T.-N. Le and S. Thomassé, Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture, arXiv preprint arXiv:1507.08208 (2015)], the conjecture was proven for trees of maximal degree 2 (i.e., paths). In particular, it was shown that in the case of paths, the conjecture holds for 24-edge-connected graphs. We improve this result showing that 3-edge-connectivity suffices, which is best possible. We disprove the conjecture for trees of maximum degree greater than two and prove a relaxed version of the conjecture that concerns decomposing the edge set of a graph into disjoint copies of two fixed trees of coprime sizes.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Notes in Discrete Mathematics
ISSN
1571-0653
e-ISSN
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Volume of the periodical
61
Issue of the periodical within the volume
August
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
7
Pages from-to
751-757
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85026765866