Related papers: The Even-Path Problem in Directed Single-Crossing-…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…
The d-Cut problem is to decide if a graph has an edge cut such that each vertex has at most d neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The d-Cut problem has been studied…
We study a constrained shortest path problem in group-labeled graphs with nonnegative edge length, called the shortest non-zero path problem. Depending on the group in question, this problem includes two types of tractable variants in…
We consider the worst-case query complexity of some variants of certain \cl{PPAD}-complete search problems. Suppose we are given a graph $G$ and a vertex $s \in V(G)$. We denote the directed graph obtained from $G$ by directing all edges in…
A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
The directed graph reachability problem takes as input an $n$-vertex directed graph $G=(V,E)$, and two distinguished vertices $s$ and $t$. The problem is to determine whether there exists a path from $s$ to $t$ in $G$. This is a canonical…
We address a problem posed by Erd\H{o}s and Hajnal in 1991, proving that for all $n \geq 600$, every $(2n+1)$-vertex graph with at least $n^2 + n + 1$ edges contains two vertices of equal degree connected by a path of length three. The…
Given a graph G and k pairs of vertices (s_1,t_1), ..., (s_k,t_k), the k-Vertex-Disjoint Paths problem asks for pairwise vertex-disjoint paths P_1, ..., P_k such that P_i goes from s_i to t_i. Schrijver [SICOMP'94] proved that the…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…
We consider the problem of computing all-pairs shortest paths in a directed graph with real weights assigned to vertices. For an $n\times n$ 0-1 matrix $C,$ let $K_{C}$ be the complete weighted graph on the rows of $C$ where the weight of…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. We show that it is NP-complete to decide whether a graph has an orientation such that…
The shortest Disjoint Path problem (SDPP) requires us to find pairwise vertex disjoint paths between k designated pairs of terminal vertices such that the sum of the path lengths is minimum. The focus here is on SDPP restricted to planar…
For two vertices $s$ and $t$ in a graph $G=(V,E)$, the next-to-shortest path is an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this paper we show that, when the graph is…
Answering a question of Erd\H{o}s and Hajnal, Chen and Ma proved that for all \(n\geq600\) every graph with \(2n + 1\) vertices and at least \(n^2 + n+1\) edges contains two vertices of equal degree connected by a path of length three. The…
We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path…