Related papers: Distances in domino flip graphs
Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a long-standing open problem. It is not known whether the problem is in P or NP-complete. We prove that two…
In this paper we systematically study various properties of the distance graph in ${\Bbb F}_q^d$, the $d$-dimensional vector space over the finite field ${\Bbb F}_q$ with $q$ elements. In the process we compute the diameter of distance…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
Let $D$ be a strongly connected digraph. The average distance $\bar{\sigma}(v)$ of a vertex $v$ of $D$ is the arithmetic mean of the distances from $v$ to all other vertices of $D$. The remoteness $\rho(D)$ and proximity $\pi(D)$ of $D$ are…
We investigate tilings of cubiculated regions with two simply connected floors by 2 x 1 x 1 bricks. More precisely, we study the flip connected component for such tilings, and provide an algebraic invariant that "almost" characterizes the…
The flip-graph of a convex polygon $\pi$ is the graph whose vertices are the triangulations of $\pi$ and whose edges correspond to flips between them. The eccentricity of a triangulation $T$ of $\pi$ is the largest possible distance in this…
We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the…
We consider the flip-width of geometric graphs, a notion of graph width recently introduced by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip-width. These include interval graphs, permutation graphs,…
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
Flips in triangulations of convex polygons arise in many different settings. They are isomorphic to rotations in binary trees, define edges in the 1-skeleton of the Associahedron and cover relations in the Tamari Lattice. The complexity of…
In this paper we introduce Yoke graphs, a family of flip graphs that generalizes several previously studied families of graphs: colored triangle free triangulations, arc permutations and caterpillars. Our main result is the computation of…
The metric dimension of a graph is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. Bailey and Meagher obtained an upper bound on the…
We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
The proximity $\pi = \pi (G)$ of a connected graph $G$ is the minimum, over all vertices, of the average distance from a vertex to all others. Similarly, the maximum is called the remoteness and denoted by $\rho = \rho (G)$. The concepts of…
The original motivation for this paper goes back to the mid-1990's, when James Propp was interested in natural situations when the number of domino tilings of a region increases if some of its unit squares are deleted. Guided in part by the…
Metric dimension is an essential parameter in graph theory that aids in addressing issues pertaining to information retrieval, localization, network design, and chemistry through the identification of the least possible number of elements…
We show that every triangulation (maximal planar graph) on $n\ge 6$ vertices can be flipped into a Hamiltonian triangulation using a sequence of less than $n/2$ combinatorial edge flips. The previously best upper bound uses $4$-connectivity…
A pseudo-triangle is a simple polygon with exactly three convex vertices, and all other vertices (if any) are distributed on three concave chains. A pseudo-triangulation~$\mathcal{T}$ of a point set~$P$ in~$\mathbb{R}^2$ is a partitioning…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…