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arXiv · 2410.00214

A combinatorial approach to phase transitions in random graph isomorphism problems

Dimitris Diamantidis·Takis Konstantopoulos·Linglong Yuan
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Abstract

We consider two independent Erd\H{o}s-R\'enyi 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 Erd\H{o}s-R\'enyi random graphs. Our approach is primarily combinatorial, naturally leading to several related problems for further exploration.

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Dimitris Diamantidis, Takis Konstantopoulos, Linglong Yuan. 2024-09-30. A combinatorial approach to phase transitions in random graph isomorphism problems. https://arxiv.org/abs/2410.00214

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