@article{13165,
  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.
As 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.
As 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.},
  author       = {Fang, Lixing and Huang, Hao and Pach, János and Tardos, Gábor and Zuo, Junchi},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory. Series A},
  number       = {10},
  publisher    = {Elsevier},
  title        = {{Successive vertex orderings of fully regular graphs}},
  doi          = {10.1016/j.jcta.2023.105776},
  volume       = {199},
  year         = {2023},
}

@article{4056,
  abstract     = {This paper proves that for every n ≥ 4 there is a convex n-gon such that the vertices of 2n - 7 vertex pairs are one unit of distance apart. This improves the previously best lower bound of ⌊ (5n - 5) 3⌋ given by Erdo{combining double acute accent}s and Moser if n ≥ 17.},
  author       = {Edelsbrunner, Herbert and Hajnal, Péter},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory Series A},
  number       = {2},
  pages        = {312 -- 316},
  publisher    = {Elsevier},
  title        = {{A lower bound on the number of unit distances between the vertices of a convex polygon}},
  doi          = {10.1016/0097-3165(91)90042-F},
  volume       = {56},
  year         = {1991},
}

@article{4098,
  abstract     = {To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.},
  author       = {Edelsbrunner, Herbert and Stöckl, Gerd},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory Series A},
  number       = {2},
  pages        = {344 -- 349},
  publisher    = {Elsevier},
  title        = {{The number of extreme pairs of finite point-sets in Euclidean spaces}},
  doi          = {10.1016/0097-3165(86)90075-0},
  volume       = {43},
  year         = {1986},
}

@article{4103,
  abstract     = {Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2).},
  author       = {Edelsbrunner, Herbert and Welzl, Emo},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory Series A},
  number       = {2},
  pages        = {159 -- 166},
  publisher    = {Elsevier},
  title        = {{On the maximal number of edges of many faces in an arrangement}},
  doi          = {10.1016/0097-3165(86)90078-6},
  volume       = {41},
  year         = {1986},
}

@article{4113,
  abstract     = {Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of fk(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on fk(n) is established. Both are nontrivial and improve bounds known before. In particular,  is shown by exhibiting special point-sets which realize that many k-sets. In addition,  is proved by the study of a combinatorial problem which is of interest in its own right.},
  author       = {Edelsbrunner, Herbert and Welzl, Emo},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory Series A},
  number       = {1},
  pages        = {15 -- 29},
  publisher    = {Elsevier},
  title        = {{On the number of line separations of a finite set in the plane}},
  doi          = {10.1016/0097-3165(85)90017-2},
  volume       = {38},
  year         = {1985},
}