Modularity of minor-free graphs
Micha{\l} Laso\'n, Ma{\l}gorzata Sulkowska
TL;DR
This paper proves that minor-free graphs with sublinear maximum degree are highly modular, with modularity approaching 1 as the graph size increases, highlighting a key structural property.
Contribution
It establishes that minor-free graphs with sublinear maximum degree are asymptotically maximally modular, a novel structural insight.
Findings
Modularity tends to 1 in large minor-free graphs with sublinear maximum degree.
Graphs with excluded minors and sublinear maximum degree are highly modular.
The result links graph minor theory with modularity properties.
Abstract
We prove that a class of graphs with an excluded minor and with the maximum degree sublinear in the number of edges is maximally modular, that is, modularity tends to 1 as the number of edges tends to infinity.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Graph Theory Research · Limits and Structures in Graph Theory