Related papers: Transition Operations over Plane Trees
A crossing-free straight-line drawing of a graph is monotone if there is a monotone path between any pair of vertices with respect to some direction. We show how to construct a monotone drawing of a tree with $n$ vertices on an $O(n^{1.5})…
A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. In this paper we present a complete classification of all…
Structured representations like graphs and parse trees play a crucial role in many Natural Language Processing systems. In recent years, the advancements in multi-turn user interfaces necessitate the need for controlling and updating these…
We consider questions related to the existence of spanning trees in graphs with the property that after the removal of any path in the tree the graph remains connected. We show that, for planar graphs, the existence of trees with this…
In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a…
We present an approach to the solution of decision problems formulated as influence diagrams. This approach involves a special triangulation of the underlying graph, the construction of a junction tree with special properties, and a message…
We prove cyclic sieving phenomena satisfied by corner-rooted plane trees (alias ordered trees). The sets of rooted plane trees that we consider are: (1) all trees with $n$ nodes; (2) all trees with $n$ nodes and $k$ leaves; (3) all trees…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a special kind of simple drawings that we call generalized…
Spanning trees are fundamental for efficient communication in networks. For fault-tolerant communication, it is desirable to have multiple spanning trees to ensure resilience against failures of nodes and edges. To this end, various notions…
In this paper we study several problems concerning the number of homomorphisms of trees. We give an algorithm for the number of homomorphisms from a tree to any graph by the Transfer-matrix method. By using this algorithm and some…
Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
As well known the rotation distance D(S,T) between two binary trees S, T of n vertices is the minimum number of rotations of pairs of vertices to transform S into T. We introduce the new operation of chain rotation on a tree, involving two…
We study groups acting vertex-transitively on connected, trivalent graphs such that stabilizers of vertices are infinite. If the action is edge-transitive, we prove that the graph has to be a tree. We analyze the case where the action is…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Tanglegrams are drawings of two rooted binary phylogenetic trees and a matching between their leaf sets. The trees are drawn crossing-free on opposite sides with their leaf sets facing each other on two vertical lines. Instead of minimizing…
Given a graph, we can form a spanning forest by first sorting the edges in some order, and then only keep edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges,…