Edge-decomposing graphs into coprime forests

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438301" target="_blank" >RIV/00216208:11320/21:10438301 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wBGGcbCYw0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wBGGcbCYw0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22638" target="_blank" >10.1002/jgt.22638</a>

Result language
angličtina
Original language name
Edge-decomposing graphs into coprime forests
Original language description
The Barat-Thomassen conjecture, recently proved in Bensmail et al. (2017), asserts that for every tree T, there is a constant c T such that every c T-edge-connected graph G with number of edges (size) divisible by the size of T admits an edge partition into copies of T (a T-decomposition). In this paper, we investigate in which case the connectivity requirement can be dropped to a minimum degree condition. For instance, it was shown in Bensmail et al. (2019) that when T is a path with k edges, there is a constant d k such that every 24-edge-connected graph G with size divisible by k and minimum degree d k has a T-decomposition. We show in this paper that when F is a coprime forest (the sizes of its components being a coprime set of integers), any graph G with sufficiently large minimum degree has an F-decomposition provided that the size of F divides the size of G (no connectivity is required). A natural conjecture asked in Bensmail et al. (2019) asserts that for a fixed tree T, any graph G of size divisible by the size of T with sufficiently high minimum degree has a T-decomposition, provided that G is sufficiently highly connected in terms of the maximal degree of T. The case of maximum degree 2 is answered by paths. We provide a counterexample to this conjecture in the case of maximum degree 3.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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