Related papers: Combinatorial characterization of upward planarity
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…
In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introduce a new tool that enables us to characterize the property…
The power graph of a group $G$ is a simple and undirected graph with vertex set $G$ and two distinct vertices are adjacent if one is a power of the other. In this article, we characterize (non-cyclic) finite groups of prime exponent and…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
A mixed graph is a graph with some directed edges and some undirected edges. We introduce the notion of mixed matroids as a generalization of mixed graphs. A mixed matroid can be viewed as an oriented matroid in which the signs over a fixed…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
We determine which properties of 2-layer drawings characterise bipartite graphs of bounded pathwidth.
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of…
A classification is given of all the countable homogeneous ordered bipartite graphs.
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
Three types of geometric structure---grid triangulations, rectangular subdivisions, and orthogonal polyhedra---can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an…
We propose efficient algorithms for enumerating the notorious combinatorial structures of maximal planar graphs, called canonical orderings and Schnyder woods, and the related classical graph drawings by de Fraysseix, Pach, and Pollack…
In this paper, we derive an upper bound for higher order eigenvalues of the normalized Laplace operator associated with a symmetric finite graph in terms of lower order eigenvalues.
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of graded vector spaces.