On $(1,2)$-step competition graphs of multipartite tournaments II
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911770171408384 |
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| author | Choi, Myungho Kim, Suh-Ryung |
| author_facet | Choi, Myungho Kim, Suh-Ryung |
| contents | A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by $C_{1,2}(D)$, of $D$. In the previous paper titled "On $(1,2)$-step competition graphs of multipartite tournaments" \cite{choi202412step} we completely characterize $C_{1,2}(D)$ for a tight multipartite tournament $D$. As an extension, in this paper, we study $(1,2)$-step competition graphs of multipartite tournaments that are not tight, which will be called loose. For a loose multipartite tournament $D$, various meaningful results are obtained in terms of $C_{1,2}(D)$ being interval and $C_{1,2}(D)$ being connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $(1,2)$-step competition graphs of multipartite tournaments II Choi, Myungho Kim, Suh-Ryung Combinatorics 05C20, 05C75 A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by $C_{1,2}(D)$, of $D$. In the previous paper titled "On $(1,2)$-step competition graphs of multipartite tournaments" \cite{choi202412step} we completely characterize $C_{1,2}(D)$ for a tight multipartite tournament $D$. As an extension, in this paper, we study $(1,2)$-step competition graphs of multipartite tournaments that are not tight, which will be called loose. For a loose multipartite tournament $D$, various meaningful results are obtained in terms of $C_{1,2}(D)$ being interval and $C_{1,2}(D)$ being connected. |
| title | On $(1,2)$-step competition graphs of multipartite tournaments II |
| topic | Combinatorics 05C20, 05C75 |
| url | https://arxiv.org/abs/2402.01986 |