On subgraphs with degrees of prescribed residues in the random graph

Asaf Ferber*, Liam Hardiman, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that with high probability the random graph (Figure presented.) has an induced subgraph of linear size, all of whose degrees are congruent to (Figure presented.) for any fixed (Figure presented.) and (Figure presented.). More generally, the same is true for any fixed distribution of degrees modulo (Figure presented.). Finally, we show that with high probability we can partition the vertices of (Figure presented.) into (Figure presented.) parts of nearly equal size, each of which induces a subgraph all of whose degrees are congruent to (Figure presented.). Our results resolve affirmatively a conjecture of Scott, who addressed the case (Figure presented.).

Original languageEnglish
Pages (from-to)192-214
Number of pages23
JournalRandom Structures and Algorithms
Volume63
Issue number1
DOIs
StatePublished - Aug 2023

Keywords

  • degree sequence
  • random graphs

Fingerprint

Dive into the research topics of 'On subgraphs with degrees of prescribed residues in the random graph'. Together they form a unique fingerprint.

Cite this