TY - JOUR

T1 - Colouring powers of cycles from random lists

AU - Krivelevich, Michael

AU - Nachmias, Asaf

N1 - Funding Information:
The authors wish to thank Maurice Cochand for posing the problem and for explaining its motivation/industrial interpretation. The first author’s research was supported in part by a USA–Israel BSF Grant and by a grant from the Israel Science Foundation.

PY - 2004/10

Y1 - 2004/10

N2 - Let Cnk be the kth power of a cycle on n vertices (i.e. the vertices of Cnk are those of the n-cycle, and two vertices are connected by an edge if their distance along the cycle is at most k). For each vertex draw uniformly at random a list of size c from a base set S of size s=s(n). In this paper we solve the problem of determining the asymptotic probability of the existence of a proper colouring from the random lists for all fixed values of c,k, and growing n.

AB - Let Cnk be the kth power of a cycle on n vertices (i.e. the vertices of Cnk are those of the n-cycle, and two vertices are connected by an edge if their distance along the cycle is at most k). For each vertex draw uniformly at random a list of size c from a base set S of size s=s(n). In this paper we solve the problem of determining the asymptotic probability of the existence of a proper colouring from the random lists for all fixed values of c,k, and growing n.

UR - http://www.scopus.com/inward/record.url?scp=4344705703&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2003.12.002

DO - 10.1016/j.ejc.2003.12.002

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AN - SCOPUS:4344705703

SN - 0195-6698

VL - 25

SP - 961

EP - 968

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 7

ER -