Colouring random subgraphs

Boris Bukh; Michael Krivelevich; Bhargav Narayanan

doi:10.1017/S0963548325000069

Colouring random subgraphs

Boris Bukh, Michael Krivelevich, Bhargav Narayanan

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We study several basic problems about colouring the p-random subgraph G_p of an arbitrary graph G, focusing primarily on the chromatic number and colouring number of G_p. In particular, we show that there exist infinitely many k-regular graphs G for which the colouring number (i.e., degeneracy) of G₁/₂ is at most k/3 + o(k) with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least k/2 − o(k).

Original language	English
Journal	Combinatorics Probability and Computing
DOIs	https://doi.org/10.1017/S0963548325000069
State	Accepted/In press - 2025

Keywords

Degeneracy
bootstrap percolation
colouring number

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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10.1017/S0963548325000069

Cite this

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title = "Colouring random subgraphs",

abstract = "We study several basic problems about colouring the p-random subgraph Gp of an arbitrary graph G, focusing primarily on the chromatic number and colouring number of Gp. In particular, we show that there exist infinitely many k-regular graphs G for which the colouring number (i.e., degeneracy) of G1/2 is at most k/3 + o(k) with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least k/2 − o(k).",

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AU - Bukh, Boris

AU - Krivelevich, Michael

AU - Narayanan, Bhargav

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AB - We study several basic problems about colouring the p-random subgraph Gp of an arbitrary graph G, focusing primarily on the chromatic number and colouring number of Gp. In particular, we show that there exist infinitely many k-regular graphs G for which the colouring number (i.e., degeneracy) of G1/2 is at most k/3 + o(k) with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least k/2 − o(k).

KW - Degeneracy

KW - bootstrap percolation

KW - colouring number

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U2 - 10.1017/S0963548325000069

DO - 10.1017/S0963548325000069

M3 - مقالة

SN - 0963-5483

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

ER -

Colouring random subgraphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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