This paper is devoted to the study of contiguity orders i.e. orders having a linear extension L such that all upper (or lower) cover sets are intervals of L. This new class is a strict generalization of both interval orders and N{free orders, and is linearly recognizable. It is proved that computing the number of contiguity extensions is #P{complete, and that the dimension of height one contigu...

This paper examines the spatial spillover effects of public transportation infrastructure on regional economy in Northeast China, “rust belt” region China. The dataset consists socioeconomic data from 47 cities area during period year 2005 through 2015. Accessibility is used as an explanatory variable to reflect influence economic development. In order avoid endogenous, queen contiguity matrix ...

This paper lays the foundations of an approach to applying Gromov’s ideas on quantitative topology to topological data analysis. We introduce the “contiguity complex”, a simplicial complex of maps between simplicial complexes defined in terms of the combinatorial notion of contiguity. We generalize the Simplicial Approximation Theorem to show that the contiguity complex approximates the homotop...

In this paper we consider a graph parameter called contiguity which aims at encoding a graph by a linear ordering of its vertices. We prove that the contiguity of cographs is unbounded but is always dominated by O(logn), where n is the number of vertices of the graph. And we prove that this bound is tight in the sense that there exists a family of cographs on n vertices whose contiguity is Ω(lo...

Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation of contiguity in the sense that every encoding achieving contiguity k induces an encoding achieving linearity k, both encoding having size Θ(k.n), where n is the number of vertices of G. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exist...