Disjoint cycles with length constraints in the disjoint union of null digraph has at most two vertices and tournament
Disjoint cycles with length constraints in the disjoint union of null digraph has at most two vertices and tournament
Siberian Electronic Mathematical Reports, 23, 2, pp. 835-853 (2026)
Abstract:
Let $D=(V,A)$ be a oriented digraph with a partition $V=K\cup I$ such that $D[I]$ is a null graph has at most two vertices and $D[K]$ is a tournament. We show in this paper that every strong $D$ with minimum out-degree 3, except the digraph $D^3_7$, contains two vertex-disjoint cycles of different lengths.
Keywords: strong digraph, tournament, vertex-disjoint cycles, cycles of different lengths, null digraph.