##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Prof. Michael Molloy

#### University of Toronto

## k-regular subgraphs near the k-core threshold of a random graph

##### Abstract:

We prove that $G_{n,p=c/n}$ whp has a $k$-regular subgraph if $c$ is at least $e^{-\Theta(k)}$ above the threshold for the appearance of a subgraph with minimum degree at least $k$; i.e. an non-empty $k$-core. In particular, this pins down the threshold for the appearance of a $k$-regular subgraph to a window of size $e^{-\Theta(k)}$.

This is a joint work with Dieter Mitsche and Pawel Pralat; see arXiv:1804.04173

### February 6, 2024

### 2:00 PM

APM 7321

Research Areas

Combinatorics****************************