Geodesic
On density conditions for transversal trees in multipartite graphs
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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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.
DOI : 10.37236/12463
Classification : 05C35, 05C80, 05D15
Mots-clés : extremal multipartite graph problems

Leila Badakhshian    ; Victor Falgas-Ravry  1   ; Maryam Sharifzadeh  1

1 Umeå Universitet 
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Leila Badakhshian; Victor  Falgas-Ravry; Maryam Sharifzadeh. On density conditions for transversal trees in multipartite graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12463

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