Lower bounds for the spanning tree numbers of two graph products
Hengzhe Li, Xueliang Li, Yaping Mao, Jun Yue
TL;DR
This paper establishes sharp lower bounds for the number of edge-disjoint spanning trees in Cartesian and Lexicographic product graphs, advancing understanding of their structural properties.
Contribution
It provides new, precise lower bounds for spanning tree numbers in specific graph products, which were previously unknown or less understood.
Findings
Sharp lower bounds for Cartesian product graphs
Sharp lower bounds for Lexicographic product graphs
Enhanced understanding of spanning tree packings in product graphs
Abstract
For any graph of order , the spanning tree packing number \emph{}, is the maximum number of edge-disjoint spanning trees contained in . In this paper, we obtain some sharp lower bounds for the spanning tree numbers of Cartesian product graphs and Lexicographic product graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory