An upper bound for the clique number using clique ceiling numbers
R. Dharmarajan, D. Ramachandran
TL;DR
This paper introduces the concept of clique ceiling numbers for graphs with a universal vertex and provides a polynomial-time algorithm to compute an upper bound for the clique number, comparing it with existing bounds.
Contribution
It proposes a novel clique ceiling number concept and an efficient algorithm to estimate the clique number in graphs with a universal vertex.
Findings
The algorithm computes upper bounds efficiently.
Clique ceiling numbers offer tighter bounds than some existing formulas.
Applicable to graphs with a universal vertex.
Abstract
In this article we present the idea of clique ceiling numbers of the vertices of a given graph that has a universal vertex. We follow up with a polynomial-time algorithm to compute an upper bound for the clique number of such a graph using clique ceiling numbers. We compare this algorithm with some upper bound formulas for the clique number.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems