Two product formulas for counting successive vertex orderings
| Autor: | Ho, Boon Suan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A vertex ordering of a graph $G$ is a bijection $\pi\colon\{1,\dots,|V(G)|\}\to V(G)$. It is successive if the induced subgraph $G[v_{\pi(1)},\dots,v_{\pi(k)}]$ is connected for each $k$. Lixing Fang, Hao Huang, J\'anos Pach, G\'abor Tardos, and Junchi Zuo [J. Comb. Theory A199 (2023), 105776] gave formulas for counting the number of successive vertex orderings for a class of graphs they called "fully regular," and conjectured that these formulas could be written as certain products involving differences or ratios of binomial coefficients in two cases: When the graph is the line graph $L(K_n^{(3)})$ of the complete $3$-uniform hypergraph, or when it is the line graph $L(K_{m,n}^{(1,2)})$ of a complete "bipartite" $3$-uniform hypergraph. In this paper, we confirm both of these conjectures. Comment: 11 pages |
| Databáze: | arXiv |
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