Geodesic
A note on the linear cycle cover conjecture of Gyárfás and Sárközy
Beka Ergemlidze1 ; Ervin Győri2 ; Abhishek Methuku1
1Central European University.
2Alfréd Rényi Institute of Mathematics and Central European University.
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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A linear cycle in a $3$-uniform hypergraph $H$ is a cyclic sequence of hyperedges such that any two consecutive hyperedges intersect in exactly one element and non-consecutive hyperedges are disjoint. Let $\alpha(H)$ denote the size of a largest independent set of $H$.We show that the vertex set of every $3$-uniform hypergraph $H$ can be covered by at most $\alpha(H)$ edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gyárfás and Sárközy.
DOI : 10.37236/7329
Classification : 05C35, 05C69
Mots-clés : loose cycles, covering, independence number

Beka Ergemlidze  1   ; Ervin Győri  2   ; Abhishek Methuku  1

1 Central European University.
2 Alfréd Rényi Institute of Mathematics and Central European University. 
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     title = {A note on the linear cycle cover conjecture of {Gy\'arf\'as} and {S\'ark\"ozy}},
     journal = {The electronic journal of combinatorics},
     year = {2018},
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     number = {2},
     doi = {10.37236/7329},
     zbl = {1390.05107},
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Beka Ergemlidze; Ervin Győri; Abhishek Methuku. A note on the linear cycle cover conjecture of Gyárfás and Sárközy. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7329

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