Vertex coloring complete multipartite graphs from random lists of size 2

• Let Ks×m be the complete multipartite graph with s parts and m vertices in each part. Assign to each vertex v of Ks×m a list L(v) of colors, by choosing each list uniformly at random from all 2-subsets of a color set C of size σ(m). In this paper we determine, for all fixed s and growing m, the asymptotic probability of the existence of a proper coloring φ, such that φ(v)∈L(v) for all v∈V(Ks×m). We show that this property exhibits a sharp threshold at σ(m)=2(s−1)m.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

List coloring; Complete multipartite graph; Random list

Publication and Content Type

ref (subject category)

art (subject category)