A combinatorial approach to phase transitions in random graph isomorphism problems

Fuente: arXiv
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Main Authors: Diamantidis, Dimitris, Konstantopoulos, Takis, Yuan, Linglong
Format: Preprint
Published: 2024
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author Diamantidis, Dimitris
Konstantopoulos, Takis
Yuan, Linglong
author_facet Diamantidis, Dimitris
Konstantopoulos, Takis
Yuan, Linglong
contents We consider two independent Erdős-Rényi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters we show a sharp asymptotic phase transition as the graph sizes tend to infinity. This extends known results for the case of uniform Erdős-Rényi random graphs. Our approach is primarily combinatorial, naturally leading to several related problems for further exploration.
format Preprint
id arxiv_https___arxiv_org_abs_2410_00214
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A combinatorial approach to phase transitions in random graph isomorphism problems
Diamantidis, Dimitris
Konstantopoulos, Takis
Yuan, Linglong
Combinatorics
Probability
60C05, 05C60, 60F99, 05A19
We consider two independent Erdős-Rényi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters we show a sharp asymptotic phase transition as the graph sizes tend to infinity. This extends known results for the case of uniform Erdős-Rényi random graphs. Our approach is primarily combinatorial, naturally leading to several related problems for further exploration.
title A combinatorial approach to phase transitions in random graph isomorphism problems
topic Combinatorics
Probability
60C05, 05C60, 60F99, 05A19
url https://arxiv.org/abs/2410.00214