Codes with structured Hamming distance in graph families

02/14/2022
by   Anna Gujgiczer, et al.
0

We investigate the maximum size of graph families on a common vertex set of cardinality n such that the symmetric difference of the edge sets of any two members of the family satisfies some prescribed condition. We solve the problem completely for infinitely many values of n when the prescribed condition is connectivity or 2-connectivity, Hamiltonicity or the containment of a spanning star. We give lower and upper bounds when it is the containment of some fixed finite graph concentrating mostly on the case when this graph is the 3-cycle or just any odd cycle. The paper ends with a collection of open problems followed by an important update in this new version of the manuscript..

READ FULL TEXT
research
07/17/2023

Phase Transitions of Structured Codes of Graphs

We consider the symmetric difference of two graphs on the same vertex se...
research
07/17/2018

Supermodular Locality Sensitive Hashes

In this work, we show deep connections between Locality Sensitive Hashab...
research
12/23/2022

Tight Bounds for Connectivity Problems Parameterized by Cutwidth

In this work we start the investigation of tight complexity bounds for c...
research
05/17/2022

The Hamilton compression of highly symmetric graphs

We say that a Hamilton cycle C=(x_1,…,x_n) in a graph G is k-symmetric, ...
research
05/22/2019

On the Critical Difference of Almost Bipartite Graphs

A set S⊆ V is independent in a graph G=( V,E) if no two vertices from S...
research
09/12/2018

Reconciling Similar Sets of Data

In this work, we consider the problem of synchronizing two sets of data ...

Please sign up or login with your details

Forgot password? Click here to reset