Related papers: 2-connecting Outerplanar Graphs without Blowing Up…
The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum…
We consider the problem of finding the minimum-weight subgraph that satisfies given connectivity requirements. Specifically, given a requirement $r \in \{0,1,2,3\}$ for every vertex, we seek the minimum-weight subgraph that contains, for…
Treewidth is an important structural graph parameter that quantifies how closely a graph resembles a tree-like structure. It has applications in many algorithmic and combinatorial problems. In this paper, we study the treewidth of outer…
Given a graph $G$, a cost function on the non-edges of $G$, and an integer $d$, the problem of finding a cheapest globally rigid supergraph of $G$ in $\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common…
We provide two constructions for $t$ edge-disjoint maximal outerplanar graphs on every number of $n \geq 4t$ vertices. The bound on the minimum number of vertices is tight. These constructions yield the existence of optimal…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…
A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be…
In this paper, we consider rainbow connection number of maximal outerplanar graphs(MOPs) on algorithmic aspect. For the (MOP) $G$, we give sufficient conditions to guarantee that $rc(G) = diam(G).$ Moreover, we produce the graph with given…
Let CMSO denote the counting monadic second order logic of graphs. We give a constructive proof that for some computable function $f$, there is an algorithm $\mathfrak{A}$ that takes as input a CMSO sentence $\varphi$, a positive integer…
For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition…
Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…
Topological drawings are representations of graphs in the plane, where vertices are represented by points, and edges by simple curves connecting the points. A drawing is simple if two edges intersect at most in a single point, either at a…
The $2$-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most fundamental and well-studied problems in the context of network design. In the problem, we are given an undirected graph $G$, and the objective is to find a…
We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these…
We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition…
We call a finite undirected graph minimally k-matchable if it has at least k distinct perfect matchings but deleting any edge results in a graph which has not. An odd subdivision of some graph G is any graph obtained by replacing every edge…
Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call $h$-Clique2Path Planarity: Given a graph $G$, whose vertices are partitioned into subsets of size at most $h$, each…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…