Related papers: Maximum Reachability Orientation of Mixed Graphs
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…
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
We consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]=\{(u,v) \in P: D {contains a} uv{-path}}$. In the {\sf Steiner Forest Orientation} problem we…
A mixed graph $G$ is a graph that consists of both undirected and directed edges. An orientation of $G$ is formed by orienting all the undirected edges of $G$, i.e., converting each undirected edge $\{u,v\}$ into a directed edge that is…
A temporal graph $\mathcal{G}=(G,\lambda)$ can be represented by an underlying graph $G=(V,E)$ together with a function $\lambda$ that assigns to each edge $e\in E$ the set of time steps during which $e$ is present. The reachability graph…
In this paper, we introduce the problem of finding an orientation of a given undirected graph that maximizes the burning number of the resulting directed graph. We show that the problem is polynomial-time solvable on K\H{o}nig-Egerv\'{a}ry…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
For distinct vertices $u$ and $v$ in a graph $G$, the {\em connectivity} between $u$ and $v$, denoted $\kappa_G(u,v)$, is the maximum number of internally disjoint $u$--$v$ paths in $G$. The {\em average connectivity} of $G$, denoted…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
A multipacking in an undirected graph $G=(V,E)$ is a set $M\subseteq V$ such that for every vertex $v\in V$ and for every integer $r\geq 1$, the ball of radius $r$ around $v$ contains at most $r$ vertices of $M$, that is, there are at most…
In 2018, Dankelmann, Gao, and Surmacs [J. Graph Theory, 88(1): 5--17, 2018] established sharp bounds on the oriented diameter of a bridgeless undirected graph and a bridgeless undirected bipartite graph in terms of vertex degree. In this…
We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree…
In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph $G$ can be preprocessed in $O(n\log^2{n}/\log\log{n})$ time,…
Many applications in graph theory are motivated by routing or flow problems. Among these problems is Steiner Orientation: given a mixed graph G (having directed and undirected edges) and a set T of k terminal pairs in G, is there an…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…