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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

  • Czech description

Classification

  • Type

    J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database

  • CEP classification

  • 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

  • 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

  • EID of the result in the Scopus database

    2-s2.0-85026765866