Related papers: Obstructions to within a few vertices or edges of …

In this paper, a polynomial time algorithm for finding the set of all cyclic subsets in a graph is presented. The concept of cyclic subsets has already been introduced in an earlier paper. The algorithm finds cyclic subsets in a graph G by…

The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First…

Given a linear ordering of the vertices of a graph, the cutwidth of a vertex $v$ with respect to this ordering is the number of edges from any vertex before $v$ (including $v$) to any vertex after $v$ in this ordering. The cutwidth of an…

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…

A bisection of a graph is a bipartition of its vertex set such that the two resulting parts differ in size by at most 1, and its size is the number of edges that connect vertices in the two parts. The perfect matching condition and…

An \emph{obstacle representation} of a graph $G$ is a straight-line drawing of $G$ in the plane together with a collection of connected subsets of the plane, called \emph{obstacles}, that block all non-edges of $G$ while not blocking any of…

We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a.s. We refine this method using new technical machinery for random $d$-regular graphs on $n$ vertices that hold not just…

Traffic bottlenecks are a set of road segments that have an unacceptable level of traffic caused by a poor balance between road capacity and traffic volume. A huge volume of trajectory data which captures real-time traffic conditions in…

In this paper we give some basic results on blocking sets on minimum size for a finite chain geometry.

We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…

Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Pattern matching is a fundamental tool for answering complex graph queries. Unfortunately, existing solutions have limited capabilities: they do not scale to process large graphs and/or support only a restricted set of search templates or…

This is an expository paper. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is contained in an even number of edges from $C$. E.g., a cycle in the sense of graph theory is a $1$-cycle, but not vice versa. It is easy to…

We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…

The orientation completion problem for a fixed class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class. Orientation completion problems have been studied recently for several…

When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…

Connected and automated vehicles have shown great potential in improving traffic mobility and reducing emissions, especially at unsignalized intersections. Previous research has shown that vehicle passing order is the key influencing factor…

We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…

In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…