Bipartite Turán number of paths and other trees

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Main Authors: Bonamy, Marthe, Leclere, Théotime, Picavet, Timothé
Format: Preprint
Published: 2025
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author Bonamy, Marthe
Leclere, Théotime
Picavet, Timothé
author_facet Bonamy, Marthe
Leclere, Théotime
Picavet, Timothé
contents We solve a recent question of Caro, Patkós and Tuza by determining the exact maximum number of edges in a bipartite connected graph as a function of the longest path it contains as a subgraph and of the number of vertices in each side of the bipartition. This was previously known only in the case where both sides of the bipartition have equal size and the longest path has size at most $5$. We also discuss possible generalizations replacing "path" with some specific types of trees.
format Preprint
id arxiv_https___arxiv_org_abs_2511_07374
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bipartite Turán number of paths and other trees
Bonamy, Marthe
Leclere, Théotime
Picavet, Timothé
Combinatorics
Discrete Mathematics
We solve a recent question of Caro, Patkós and Tuza by determining the exact maximum number of edges in a bipartite connected graph as a function of the longest path it contains as a subgraph and of the number of vertices in each side of the bipartition. This was previously known only in the case where both sides of the bipartition have equal size and the longest path has size at most $5$. We also discuss possible generalizations replacing "path" with some specific types of trees.
title Bipartite Turán number of paths and other trees
topic Combinatorics
Discrete Mathematics
url https://arxiv.org/abs/2511.07374