Geodesic
Covering 3-coloured random graphs with monochromatic trees
Yoshiharu Kohayakawa1 ; Walner Mendonça2 ; Guilherme Mota3 ; Bjarne Schülke4 ; Yoshiharu Kohayakawa ; Walner Mendonça ; Guilherme Mota ; Bjarne Schülke
1Departamento de Ciência da Computação, Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil
2Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
3Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, Brazil
4Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 871-875 
Yoshiharu Kohayakawa; Walner Mendonça; Guilherme Mota; Bjarne Schülke; Yoshiharu Kohayakawa; Walner Mendonça; Guilherme Mota; Bjarne Schülke. Covering 3-coloured random graphs with monochromatic trees. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 871-875. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a79/
@article{AMUC_2019_88_3_a79,
     author = {Yoshiharu Kohayakawa and Walner Mendon\c{c}a and Guilherme Mota and Bjarne Sch\"ulke and Yoshiharu Kohayakawa and Walner Mendon\c{c}a and Guilherme Mota and Bjarne Sch\"ulke},
     title = { Covering 3-coloured random graphs with monochromatic trees},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {871--875},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a79/}
}
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Voir la notice de l'article provenant de la source Comenius University

We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for $p\gg \left(\frac{\ln n}{n}\right)^{1/6}$ in any $3$-colouring of the random graph $G(n,p)$ we can find $3$ monochromatic trees such that their union covers all vertices. This improves, for three colours, a result of Buci\'c, Kor\'andi and Sudakov [Covering random graphs by monochromatic trees and Helly-type results for hypergraphs, arXiv:1902.05055].