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Free Edge Lengths in Plane Graphs

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The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al.

Lukas Fritz Felix Vogl

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Elsevier2024

A full characterization of invariant embeddability of unimodular planar graphs

Laszlo Marton Toth

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

WILEY2023

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Jana Tabea Cslovjecsek

We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

Ottawa2023

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

IEEE COMPUTER SOC2022

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We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

2022

Scalable Robust Graph Embedding with Spark

Karl Aberer, Quoc Viet Hung Nguyen, Chi Thang Duong, Trung-Dung Hoang

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to larg ...

ASSOC COMPUTING MACHINERY2021

Efficient Streaming Subgraph Isomorphism with Graph Neural Networks

Karl Aberer, Quoc Viet Hung Nguyen, Chi Thang Duong, Trung-Dung Hoang

Queries to detect isomorphic subgraphs are important in graph-based data management. While the problem of subgraph isomorphism search has received considerable attention for the static setting of a single query, or a batch thereof, existing approaches do n ...

ASSOC COMPUTING MACHINERY2021

Graph Embeddings for One-pass Processing of Heterogeneous Queries

Karl Aberer, Quoc Viet Hung Nguyen, Chi Thang Duong

Effective information retrieval (IR) relies on the ability to comprehensively capture a user's information needs. Traditional IR systems are limited to homogeneous queries that define the information to retrieve by a single modality. Support for heterogene ...

IEEE COMPUTER SOC2020

Let F be a fixed graph. The rainbow Turan number of F is defined as the maximum number of edges in a graph on n vertices that has a proper edge-coloring with no rainbow copy of F (i.e., a copy of F all of whose edges have different colours). The systematic ...

ELECTRONIC JOURNAL OF COMBINATORICS2019

Thrackles: An improved upper bound

János Pach, Radoslav Fulek

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