Large chromatic number and Ramsey graphs
Csaba Bir\'o, Zolt\'an F\"uredi, Sogol Jahanbekam
TL;DR
This paper derives an implicit formula for the minimum clique size of n-vertex graphs with a given chromatic number c, specifically when c is at least (n+3)/2, utilizing Ramsey graphs.
Contribution
It provides an exact, implicit formula for the minimum clique size in graphs with high chromatic number using Ramsey graph constructions.
Findings
Derived an implicit formula for Q(n,c) for c ≥ (n+3)/2
Utilized Ramsey graphs to establish bounds on clique sizes
Enhanced understanding of the relationship between chromatic number and clique size
Abstract
Let Q(n,c) denote the minimum clique size an n-vertex graph can have if its chromatic number is c. Using Ramsey graphs we give an exact, albeit implicit, formula for the case c is at least (n+3)/2.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Advanced Topology and Set Theory