Decomposing graphs into paths and trees

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Decomposing graphs into paths and trees

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Decomposing graphs into paths and trees

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Notes in Discrete Mathematics

ISSN

1571-0653

e-ISSN

—

Svazek periodika

61

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

751-757

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85026765866