---
res:
bibo_abstract:
- "A graph G=(V, E) is called fully regular if for every independent set I c V,
the number of vertices in V\\I that are not connected to any element of I depends
only on the size of I. A linear ordering of the vertices of G is called successive
if for every i, the first i vertices induce a connected subgraph of G. We give
an explicit formula for the number of successive vertex orderings of a fully regular
graph.\r\nAs an application of our results, we give alternative proofs of two
theorems of Stanley and Gao & Peng, determining the number of linear edge orderings
of complete graphs and complete bipartite graphs, respectively, with the property
that the first i edges induce a connected subgraph.\r\nAs another application,
we give a simple product formula for the number of linear orderings of the hyperedges
of a complete 3-partite 3-uniform hypergraph such that, for every i, the first
i hyperedges induce a connected subgraph. We found similar formulas for complete
(non-partite) 3-uniform hypergraphs and in another closely related case, but we
managed to verify them only when the number of vertices is small.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Lixing
foaf_name: Fang, Lixing
foaf_surname: Fang
- foaf_Person:
foaf_givenName: Hao
foaf_name: Huang, Hao
foaf_surname: Huang
- foaf_Person:
foaf_givenName: János
foaf_name: Pach, János
foaf_surname: Pach
foaf_workInfoHomepage: http://www.librecat.org/personId=E62E3130-B088-11EA-B919-BF823C25FEA4
- foaf_Person:
foaf_givenName: Gábor
foaf_name: Tardos, Gábor
foaf_surname: Tardos
- foaf_Person:
foaf_givenName: Junchi
foaf_name: Zuo, Junchi
foaf_surname: Zuo
bibo_doi: 10.1016/j.jcta.2023.105776
bibo_issue: '10'
bibo_volume: 199
dct_date: 2023^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0097-3165
- http://id.crossref.org/issn/1096-0899
dct_language: eng
dct_publisher: Elsevier@
dct_title: Successive vertex orderings of fully regular graphs@
...