Clique colouring of binomial random graphs
Colin McDiarmid, Dieter Mitsche, Pawel Pralat
TL;DR
This paper investigates the asymptotic behavior of the clique chromatic number in binomial random graphs G(n,p), revealing a step function pattern as a function of the average degree for various edge probabilities.
Contribution
It provides new insights into the asymptotic properties of clique colourings in G(n,p), highlighting a step function pattern in the clique chromatic number.
Findings
Clique chromatic number exhibits a step function pattern
Asymptotic analysis for a wide range of p in G(n,p)
Characterization of the typical clique chromatic number behavior
Abstract
A clique colouring of a graph is a colouring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colours in such a colouring is the clique chromatic number. In this paper, we study the asymptotic behaviour of the clique chromatic number of the random graph G(n,p) for a wide range of edge-probabilities p=p(n). We see that the typical clique chromatic number, as a function of the average degree, forms an intriguing step function.
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Taxonomy
TopicsLimits and Structures in Graph Theory · graph theory and CDMA systems · Advanced Graph Theory Research