Work

The Asymptotic χ‐Boundedness of Hereditary Families

Year: 2026

Type: article

Abstract: ABSTRACT A family of graphs is asymptotically ‐bounded with bounding function if almost every graph in the family satisfies . A graph is ‐free if it does not contain as an induced subgraph. We ask which hereditary families are asymptotically ‐bounded, and discuss some related questions. We show that for every tree , almost all ‐free graphs satisfy . We show that for every cycle except , almost every ‐free graph satisfies . We show that the ‐free graphs are asymptotically ‐bounded with bounding function .

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.70119

Authors: Bruce Reed, Yelena Yuditsky

Institutions: Institute of Mathematics, Academia Sinica, Academia Sinica, University of Leeds

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4414894572

FWCI: 2.401

Cites: 24

Cited by: 2

Related to: 10