Transversal Structures in Graph Systems: A Survey
| Autor: | Sun, Wanting, Wang, Guanghui, Wei, Lan |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\phi :E(H)\rightarrow [m]$ such that $e \in E(G_{\phi(e)})$ 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. Comment: 24 pages, 2 figures |
| Databáze: | arXiv |
| Externí odkaz: |
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