Related papers: Computational complexity of distance edge labeling

For any fixed positive integer $r$ and a given budget $k$, the $r$-\textsc{Eigenvalue Vertex Deletion} ($r$-EVD) problem asks if a graph $G$ admits a subset $S$ of at most $k$ vertices such that the adjacency matrix of $G\setminus S$ has at…

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

In a graph $A$, the measure $|M_g^A(f)|=m_g^A(f)$ for each arbitrary edge $f=gh$ counts the edges in $A$ closer to $g$ than $h$. $A$ is termed an edge quasi-$\lambda$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where…

We prove that it is NP-complete to determine whether there exists a distance-2 edge coloring (strong edge coloring) with 5 colors of a bipartite 2-inductive graph with girth 6 and maximum degree 3.

A distance magic labeling of an $n$-dimensional hypercube is a labeling of its vertices by natural numbers from $\{0, \ldots, 2^n-1\}$, such that for all vertices $v$ the sum of the labels of the neighbors of $v$ is the same. Such a…

Given a set of $n$ points (sites) inside a rectangle $R$ and $n$ points (label locations or ports) on its boundary, a boundary labeling problem seeks ways of connecting every site to a distinct port while achieving different labeling…

A {\em faithful (unit) distance graph} in $\mathbb{R}^d$ is a graph whose set of vertices is a finite subset of the $d$-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is…

The problem of determining whether a graph $G$ can be realized as a unit-distance graph in $\mathbb{Z}^2$ is NP-complete. As far as we can tell, a proof of this result has never been written up. We prove NP-completeness of this problem by…

There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…

Let G = (V, E, L) be an edge-labeled graph such that V is the set of vertices, E is the set of edges, L is the set of labels (colors) and each edge e \in E has a label l(e) associated; The goal of the minimum labeling global cut problem…

The complexity of graph homomorphisms has been a subject of intense study [11, 12, 4, 42, 21, 17, 6, 20]. The partition function $Z_{\mathbf A}(\cdot)$ of graph homomorphism is defined by a symmetric matrix $\mathbf A$ over $\mathbb C$. We…

We tackle the problem of semantic boundary prediction, which aims to identify pixels that belong to object(class) boundaries. We notice that relevant datasets consist of a significant level of label noise, reflecting the fact that precise…

Given a graph G=(V,E) with a label set L = {l_1, l_2, ..., l_q}, in which each edge has a label from L, a source s in V, and a sink t in V, the Min Label s-t Cut problem asks to pick a set L' subseteq L of labels with minimized cardinality,…

Multi-label learning deals with the classification problems where each instance can be assigned with multiple labels simultaneously. Conventional multi-label learning approaches mainly focus on exploiting label correlations. It is usually…

We study $\tau$-Bounded-Density Edge Deletion ($\tau$-BDED), where given an undirected graph $G$, the task is to remove as few edges as possible to obtain a graph $G'$ where no subgraph of $G'$ has density more than $\tau$. The density of a…

An L(2, 1)-labeling of a graph is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive numbers differed by at least 2, and vertices at distance 2 are assigned distinct numbers. The L(2, 1)-labeling…

Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…

Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is…

The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…

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…