The structure of graphs with a vital linkage of order 2
Dillon Mayhew, Geoff Whittle, Stefan H. M. van Zwam
TL;DR
This paper characterizes graphs with a vital linkage of order 2, identifying them as specific minors within a family of highly structured graphs, advancing understanding of graph connectivity and linkage properties.
Contribution
It provides a new characterization of graphs with a vital linkage of order 2 through minors of structured graphs, enriching linkage theory.
Findings
Graphs with a vital linkage of order 2 are characterized as certain minors.
The characterization involves highly structured graphs.
The results deepen understanding of graph connectivity and linkage structures.
Abstract
A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph Labeling and Dimension Problems