Minors in expanding graphs
Michael Krivelevich, Benny Sudakov
TL;DR
This paper provides nearly optimal bounds on the size of clique-minors in expanding graphs, demonstrating that certain classes of graphs without short cycles contain large clique-minors, thus resolving open questions.
Contribution
It extends previous results to establish tight bounds on clique-minors in expanding graphs and applies these to H-free graphs and graphs without short cycles.
Findings
Large clique-minors exist in graphs without short cycles.
H-free graphs contain large clique-minors.
Resolved open questions regarding clique-minors in specific graph classes.
Abstract
Extending several previous results we obtained nearly tight estimates on the maximum size of a clique-minor in various classes of expanding graphs. These results can be used to show that graphs without short cycles and other H-free graphs contain large clique-minors, resolving some open questions in this area.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems