# An upper bound for the clique number using clique ceiling numbers

## 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.

## Key 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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Source: https://tomesphere.com/paper/1906.00589