The Set Chromatic Number of Random Graphs

Abstract

In this paper we study the set chromatic number of a random graph G(n, p) for a wide range of p = p(n). We show that the set chromatic number, as a function of p, forms an intriguing zigzag shape.

Clique coloring of binomial random graphs

“…Note that p = p ( n ) may (and usually does) tend to zero as n tends to infinity. The behavior of many coloring problems has been investigated for 𝒢( n , p ): the classic chromatic number has been intensively studied, see and the references therein; the list chromatic number (known also as the choice number) was studied among others in , and other variants were analyzed recently in .…”

“…The binomial random graph G(n, p) is the random graph G with vertex set [n] in which every pair {i, j} ∈ [n] 2 appears independently as an edge in G with probability p. Note that p = p(n) may (and usually does) tend to zero as n tends to infinity. The behaviour of many colouring problems has been investigated for G(n, p): the classic chromatic number has been intensively studied, see [12,14] and the references therein; the list chromatic number (known also as the choice number) was studied among others in [17,25], and other variants were analysed recently in [8,6] and [10].…”