Vertex-disjoint cycles of different lengths in tournaments of cycles

Vertex-disjoint cycles of different lengths in tournaments of cycles

Hung L. X.
Siberian Electronic Mathematical Reports, 22, No. 1, pp. 46-53 (2024)
Full-text

УДК 519.17  
DOI: 10.33048/semi.2025.22.004  
MSC 05C20, 05C38

Abstract: 

We show in this paper that every tournament of $k$ cycles $D=(V,A)$ with $k\ge 2$ and minimum out-degree 3, except the digraph $D^3_8$, contains two disjoint cycles of different lengths.

 

Keywords: digraph, tournament of cycles, vertex-disjoint cycles, cycles of different lengths.