Tur\'an graphs with bounded matching number
Noga Alon, Peter Frankl
TL;DR
This paper characterizes the maximum number of edges in graphs with given vertices, bounded matching number, and clique number, providing a comprehensive extremal graph theory result.
Contribution
It determines the maximum edges in graphs constrained by matching and clique numbers for all parameter values, extending extremal graph theory.
Findings
Explicit formulas for maximum edges based on parameters
Complete characterization for all admissible parameters
Generalization of classical extremal results
Abstract
We determine the maximum possible number of edges of a graph with vertices, matching number at most and clique number at most for all admissible values of the parameters.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · Advanced Graph Theory Research