A Kruskal-Katona Type Theorem for Graphs
Andy Frohmader
TL;DR
This paper establishes new bounds on consecutive and non-consecutive clique numbers in graphs, improving upon classical Kruskal-Katona bounds, with potential applications in graph theory and combinatorics.
Contribution
It introduces a novel bound on consecutive clique numbers that often surpasses the Kruskal-Katona theorem, along with a bound on non-consecutive clique numbers.
Findings
New bounds on consecutive clique numbers are tighter than Kruskal-Katona bounds.
Bound on non-consecutive clique numbers is also established.
Results demonstrate improved estimates in graph clique analysis.
Abstract
A bound on consecutive clique numbers of graphs is established. This bound is evaluated and shown to often be much better than the bound of the Kruskal-Katona theorem. A bound on non-consecutive clique numbers is also proven.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Advanced Graph Theory Research