DeepAI AI Chat
Log In Sign Up

Obstructions to a small hyperbolicity in Helly graphs

09/08/2017
by   Feodor F. Dragan, et al.
Kent State University
0

It is known that for every graph G there exists the smallest Helly graph H(G) into which G isometrically embeds ( H(G) is called the injective hull of G) such that the hyperbolicity of H(G) is equal to the hyperbolicity of G. Motivated by this, we investigate structural properties of Helly graphs that govern their hyperbolicity and identify three isometric subgraphs of the King-grid as structural obstructions to a small hyperbolicity in Helly graphs.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/28/2020

Injective hulls of various graph classes

A graph is Helly if its disks satisfy the Helly property, i.e., every fa...
08/27/2019

Corona product of signed graphs and its application to signed network modelling

The notion of corona of two graphs was introduced by Frucht and Harary i...
12/22/2021

Burling graphs revisited, part III: Applications to χ-boundedness

The Burling sequence is a sequence of triangle-free graphs of unbounded ...
08/24/2018

Future Automation Engineering using Structural Graph Convolutional Neural Networks

The digitalization of automation engineering generates large quantities ...
02/15/2023

SynGraphy: Succinct Summarisation of Large Networks via Small Synthetic Representative Graphs

We describe SynGraphy, a method for visually summarising the structure o...
09/04/2022

A Prufer-Sequence Based Representation of Large Graphs for Structural Encoding of Logic Networks

The pervasiveness of graphs in today's real life systems is quite eviden...
10/30/2018

The 2-domination and Roman domination numbers of grid graphs

We investigate the 2-domination number for grid graphs, that is the size...