Concept

Degree (graph theory)

Related publications (42)

Better Trees for Santa Claus

Etienne Michel François Bamas, Lars Rohwedder

We revisit the problem max-min degree arborescence, which was introduced by Bateni et al. [STOC'09] as a central special case of the general Santa Claus problem, which constitutes a notorious open question in approximation algorithms. In the former problem ...

New York2023

One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

The metric dimension of a graph G is the minimal size of a subset R of vertices of G that, upon reporting their graph distance from a distinguished (source) vertex v⋆, enable unique identification of the source vertex v⋆ among all possible vertices of G. I ...

2021

The problem of generating a minimal implementation of a given Boolean function is called exact synthesis. The parameter to be minimized is often the total number of gates used for the implementation. The exact synthesis engine is considered an essential to ...

IEEE COMPUTER SOC2020

Improved Ramsey-type results for comparability graphs

Istvan Tomon, Dániel József Korándi

Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...

CAMBRIDGE UNIV PRESS2020

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...

ELSEVIER SCIENCE BV2019

A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...

2019

A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Subgraph Problem

We present a factors 4/3 approximation algorithm for the problem of finding a minimum 2-edge connected spanning subgraph of a given undirected multigraph. The algorithm is based upon a reduction to a restricted class of graphs. In these graphs, the approxi ...

2019

The recently proposed concept of metamaterials has opened exciting venues to control wave-matter interactions in unprecedented ways. Here, we demonstrate the relevance of metamaterials for inducing acoustic birefringence, a phenomenon which has already fou ...

2019

This work examines the problem of graph learning over a diffusion network when measurements can only be gathered from a limited fraction of agents (latent regime). Under this selling, most works in the literature rely on a degree of sparsity to provide gua ...

IEEE2018

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