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Abstract
Magnant and Martin [24] conjectured that every dregular graph on n vertices can be covered by n/(d + 1) vertexdisjoint paths. Gruslys and Letzter [11] verified this conjecture in the dense case, even for cycles rather than paths. We prove the analogous result for directed graphs and oriented graphs, that is, for all α > 0, there exists n_{0} = n_{0}(α) such that every dregular digraph on n vertices with d ≥ αn can be covered by at most n/(d + 1) vertexdisjoint cycles. Moreover if G is an oriented graph, then n/(2d + 1) cycles suffice. This also establishes Jackson’s long standing conjecture [14] for large n that every dregular oriented graph on n vertices with n ≤ 4d + 1 is Hamiltonian.
Original language  English 

Title of host publication  EUROCOMB’23 
Publisher  Masaryk University Press 
Pages  18 
Number of pages  8 
DOIs  
Publication status  Published  28 Aug 2023 
Event  European Conference on Combinatorics, Graph Theory and Applications  Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic Duration: 28 Aug 2023 → 1 Sept 2023 https://iuuk.mff.cuni.cz/events/conferences/eurocomb23/ 
Publication series
Name  European Conference on Combinatorics, Graph Theory and Applications 

Publisher  Masaryk University Press 
Number  12 
ISSN (Electronic)  27883116 
Conference
Conference  European Conference on Combinatorics, Graph Theory and Applications 

Abbreviated title  EUROCOMB'23 
Country/Territory  Czech Republic 
City  Prague 
Period  28/08/23 → 1/09/23 
Internet address 
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