Work

Forbidden Subgraphs and Complete Partitions

Year: 2025

Type: article

Abstract: A graph is called an $(r,k)$-graph if its vertex set can be partitioned into $r$ parts, each having at most $k$ vertices and there is at least one edge between any two parts. Let $f(r,H)$ be the minimum $k$ for which there exists an $H$-free $(r,k)$-graph. In this paper we build on the work of Axenovich and Martin, obtaining improved bounds on this function when $H$ is a complete bipartite graph or an even cycle. Some of these bounds are best possible up to a constant factor and confirm a conjecture of Axenovich and Martin in several cases.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12354

Authors: John Byrne, Michael Tait, Craig Timmons

Institutions: University of Delaware, Villanova University, California State University, Sacramento

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Algebraic Methods in Extremal Combinatorics, Spectral and Extremal Graph Theory