Multipartite tournaments in which any two vertices have an $(i,j)$-step common out-neighbor
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916424672346112 |
|---|---|
| author | Choi, Myungho Kim, Suh-Ryung |
| author_facet | Choi, Myungho Kim, Suh-Ryung |
| contents | We say that a digraph $D$ is $(i,j)$-step competitive if any two vertices have an $(i,j)$-step common out-neighbor in $D$ and that a graph $G$ is $(i,j)$-step competitively orientable if there exists an $(i,j)$-step competitive orientation of $G$.
In [Choi et al. Competitively orientable complete multipartite graphs. Discrete Mathematics, 345(9):112950, 2022], Choi et al. introduce the notion of competitive digraph and completely characterize competitively orientable complete multipartite graphs in terms of the sizes of its partite sets. Here, a competitive digraph means a $(1,1)$-step competitive digraph. In this paper, the result of Choi et al. has been extended to a general characterization of $(i,j)$-step competitively orientable complete multipartite graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multipartite tournaments in which any two vertices have an $(i,j)$-step common out-neighbor Choi, Myungho Kim, Suh-Ryung Combinatorics 05C20, 05C75 We say that a digraph $D$ is $(i,j)$-step competitive if any two vertices have an $(i,j)$-step common out-neighbor in $D$ and that a graph $G$ is $(i,j)$-step competitively orientable if there exists an $(i,j)$-step competitive orientation of $G$. In [Choi et al. Competitively orientable complete multipartite graphs. Discrete Mathematics, 345(9):112950, 2022], Choi et al. introduce the notion of competitive digraph and completely characterize competitively orientable complete multipartite graphs in terms of the sizes of its partite sets. Here, a competitive digraph means a $(1,1)$-step competitive digraph. In this paper, the result of Choi et al. has been extended to a general characterization of $(i,j)$-step competitively orientable complete multipartite graphs. |
| title | Multipartite tournaments in which any two vertices have an $(i,j)$-step common out-neighbor |
| topic | Combinatorics 05C20, 05C75 |
| url | https://arxiv.org/abs/2410.04379 |