Arc-disjoint Steiner Cycles in Digraphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909046625271808 |
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| author | Bai, Jie Sun, Yuefang Wang, Chuchu Yu, Shanshan |
| author_facet | Bai, Jie Sun, Yuefang Wang, Chuchu Yu, Shanshan |
| contents | Let $D=(V(D), A(D))$ be a digraph of order $n$ and let $S\subseteq V(D)$ with $2\leq |S|\leq n$. A directed cycle $C$ of $D$ is called a directed $S$-Steiner cycle (or, an $S$-cycle for short) if $S\subseteq V(C)$. Steiner cycles have applications in reliable designs for telecommunication and transportation networks. Two $S$-cycles are called arc-disjoint if they have no common arcs. We use $λ_{S}^{c}(D)$ to denote the maximum number of pairwise arc-disjoint $S$-cycles in $D$. The directed cycle $k$-arc-connectivity of $D$ is defined as $$λ_{k}^{c} (D)=\min\left \{ λ_{S}^{c}(D)\mid S\subseteq V(D),\left | S \right | =k,2\le k\le n \right \}.$$
In this paper, we determine the complexity for $λ_{S}^{c} (D)$ on Eulerian digraphs, planar digraphs and symmetric digraphs. We also obtain exact values of $λ_{k}^{c} (D)$ on complete digraphs, complete bipartite digraphs and regular complete multipartite digraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arc-disjoint Steiner Cycles in Digraphs Bai, Jie Sun, Yuefang Wang, Chuchu Yu, Shanshan Combinatorics Let $D=(V(D), A(D))$ be a digraph of order $n$ and let $S\subseteq V(D)$ with $2\leq |S|\leq n$. A directed cycle $C$ of $D$ is called a directed $S$-Steiner cycle (or, an $S$-cycle for short) if $S\subseteq V(C)$. Steiner cycles have applications in reliable designs for telecommunication and transportation networks. Two $S$-cycles are called arc-disjoint if they have no common arcs. We use $λ_{S}^{c}(D)$ to denote the maximum number of pairwise arc-disjoint $S$-cycles in $D$. The directed cycle $k$-arc-connectivity of $D$ is defined as $$λ_{k}^{c} (D)=\min\left \{ λ_{S}^{c}(D)\mid S\subseteq V(D),\left | S \right | =k,2\le k\le n \right \}.$$ In this paper, we determine the complexity for $λ_{S}^{c} (D)$ on Eulerian digraphs, planar digraphs and symmetric digraphs. We also obtain exact values of $λ_{k}^{c} (D)$ on complete digraphs, complete bipartite digraphs and regular complete multipartite digraphs. |
| title | Arc-disjoint Steiner Cycles in Digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.15773 |