Transversal Structures in Graph Systems: A Survey
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915935450824704 |
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| author | Sun, Wanting Wang, Guanghui Wei, Lan |
| author_facet | Sun, Wanting Wang, Guanghui Wei, Lan |
| contents | Given a system $\mathcal{G} =\{G_1,G_2,\dots,G_m\}$ of graphs/digraphs/hypergraphs on the common vertex set $V$ of size $n$, an $m$-edge graph/digraph/hypergraph $H$ on $V$ is transversal in $\mathcal{G}$ if there exists a bijection $ϕ:E(H)\rightarrow [m]$ such that $e \in E(G_{ϕ(e)})$ for all $e\in E(H)$. In this survey, we consider extremal problems for transversal structures in graph systems. More precisely, we summarize some sufficient conditions that ensure the existence of transversal structures in graph/digraph/hypergraph systems, which generalize several classical theorems in extremal graph theory to transversal version. We also include a number of conjectures and open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transversal Structures in Graph Systems: A Survey Sun, Wanting Wang, Guanghui Wei, Lan Combinatorics 05C35 Given a system $\mathcal{G} =\{G_1,G_2,\dots,G_m\}$ of graphs/digraphs/hypergraphs on the common vertex set $V$ of size $n$, an $m$-edge graph/digraph/hypergraph $H$ on $V$ is transversal in $\mathcal{G}$ if there exists a bijection $ϕ:E(H)\rightarrow [m]$ such that $e \in E(G_{ϕ(e)})$ for all $e\in E(H)$. In this survey, we consider extremal problems for transversal structures in graph systems. More precisely, we summarize some sufficient conditions that ensure the existence of transversal structures in graph/digraph/hypergraph systems, which generalize several classical theorems in extremal graph theory to transversal version. We also include a number of conjectures and open problems. |
| title | Transversal Structures in Graph Systems: A Survey |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2412.01121 |