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The induced-$P_4$-free process

Year: 2026

Type: preprint

Abstract: We study the random induced-$P_4$-free graph process. Let $e_1,\ldots,e_N$, where $N=\binom{n}{2}$, be a uniformly random ordering of the edges of $K_n$. Starting from the empty graph $G_0$, we add $e_{m+1}$ whenever $G_m+e_{m+1}$ contains no induced $P_4$, and otherwise leave the graph unchanged. We show that the terminal graph is a trivially perfect graph and we describe the structure and distribution of the connected components of the terminal graph $G_N$. Consequently, we derive the limiting values of several natural graph parameters. In particular, the terminal graph $G_N$ has $Θ(n)$ edges.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.18648

Authors: Lou, Hongyi, Song, Xinzhe, Yan, Guiying

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203885671

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