Related papers: Optimal Index Codes with Near-Extreme Rates
The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…
An identifying code $C$ of a graph $G$ is a dominating set of $G$ such that any two distinct vertices of $G$ have distinct closed neighbourhoods within $C$. These codes have been widely studied for over two decades. We give an improvement…
The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches,…
In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and…
This paper presents a study on two data structures that have been used to model several problems in computer science: and/or graphs and x-y graphs. An and/or graph is an acyclic digraph containing a source, such that every vertex v has a…
Recently, there have been found new relations between the zero forcing number and the minimum rank of a graph with the algebraic co-rank. We continue on this direction by giving a characterization of the graphs with real algebraic co-rank…
We study the secure decentralized Pliable Index CODing (PICOD) problem with circular side information sets at the users. The security constraint forbids every user to decode more than one message while a decentralized setting means there is…
A \emph{co-bipartite chain} graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cut problem (MaxCut) is NP-Hard in…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…
Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
For a simple graph, the minimum rank problem is to determine the smallest rank among the symmetric matrices whose off-diagonal nonzero entries occur in positions corresponding to the edges of the graph. Bounds on this minimum rank (and on…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
We investigate how small the Randi\'c index of a graph can be in terms of its matching number, and prove several results. We give best-possible linear bounds for graphs of small excess and for subcubic graphs; in the former case the size of…
The {\sc weak 2-linkage} problem for digraphs asks for a given digraph and vertices $s_1,s_2,t_1,t_2$ whether $D$ contains a pair of arc-disjoint paths $P_1,P_2$ such that $P_i$ is an $(s_i,t_i)$-path. This problem is NP-complete for…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this…
Consider a radio access network wherein a base-station is required to deliver a set of order-constrained messages to a set of users over independent erasure channels. This paper studies the delivery time reduction problem using instantly…