Work

On Density Conditions for Transversal Trees in Multipartite Graphs

Year: 2024

Type: article

Abstract: Let $G$ be an $r$-partite graph such that the edge density between any two parts is at least $\alpha$. How large does $\alpha$ need to be to guarantee that $G$ contains a connected transversal, that is, a tree on $r$ vertices meeting each part in one vertex? And what if instead we want to guarantee the existence of a Hamiltonian transversal? In this paper we initiate the study of such extremal multipartite graph problems, obtaining a number of results and providing many new constructions, conjectures and further questions.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12463

Authors: Leila Badakhshian, Victor Falgas-Ravry, Maryam Sharifzadeh

Institution: Umeå University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Vetenskapsrådet, Umeå Universitet

Award: Extremal problems for multicoloured graphs and locally dependent percolation