
TL;DR
This paper establishes precise conditions under which bipartite graphs contain specific structured matchings called $(s,t)$-matchings, generalizing and confirming a conjecture in the field.
Contribution
The paper provides sharp criteria for the existence of $(s,t)$-matchings in bipartite graphs, including a proof of a previously conjectured case.
Findings
Derived sharp conditions for $(s,t)$-matchings
Confirmed a conjecture by Bonacina et al.
Extended understanding of structured matchings in bipartite graphs
Abstract
An -matching in a bipartite graph is a subset of the edges such that each component of is a tree with at most edges and each vertex in has neighbours in . We give sharp conditions for a bipartite graph to contain an -matching. As a special case, we prove a conjecture of Bonacina, Galesi, Huynh and Wollan \cite{CNF}.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph theory and applications
