TY - JOUR

T1 - T-choosability in graphs

AU - Alon, Noga

AU - Zaks, Ayal

N1 - Funding Information:
supported in part by a grant from the Israel Science Foundation

PY - 1998/3/2

Y1 - 1998/3/2

N2 - Given a set of nonnegative integers T. and a function ℒ which assigns a set of integers S(v) to each vertex v of a graph G, an ℒ-list T-coloring c of G is a vertex-coloring (with positive integers) of G such that c(v) ∈ S(v) whenever v ∈ V(G) and |c(u) - c(w)| ∉ T whenever (u,w) ∈ E(G). For a fixed T, the T-choice number T-ch(G) of a graph G is the smallest number A such that G has an ℒ-list T-coloring for every collection of sets S(v) of size k each. Exact values and bounds on the Tr,s-choice numbers where Tr,s = {0,s,2s,...,rs} are presented for even cycles, notably that Tr,s-ch(C2n) = 2r + 2 if n ≥ r + 1. More bounds are obtained by applying algebraic and probabilistic techniques, such as that T-ch(C2n)≤2|T| if 0 ∈ T, and c1r log n ≤ Tr,s-ch(Kn,n) ≤ c2r log n for some absolute positive constants c1,c2.

AB - Given a set of nonnegative integers T. and a function ℒ which assigns a set of integers S(v) to each vertex v of a graph G, an ℒ-list T-coloring c of G is a vertex-coloring (with positive integers) of G such that c(v) ∈ S(v) whenever v ∈ V(G) and |c(u) - c(w)| ∉ T whenever (u,w) ∈ E(G). For a fixed T, the T-choice number T-ch(G) of a graph G is the smallest number A such that G has an ℒ-list T-coloring for every collection of sets S(v) of size k each. Exact values and bounds on the Tr,s-choice numbers where Tr,s = {0,s,2s,...,rs} are presented for even cycles, notably that Tr,s-ch(C2n) = 2r + 2 if n ≥ r + 1. More bounds are obtained by applying algebraic and probabilistic techniques, such as that T-ch(C2n)≤2|T| if 0 ∈ T, and c1r log n ≤ Tr,s-ch(Kn,n) ≤ c2r log n for some absolute positive constants c1,c2.

UR - http://www.scopus.com/inward/record.url?scp=0042624299&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(97)00124-8

DO - 10.1016/S0166-218X(97)00124-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0042624299

SN - 0166-218X

VL - 82

SP - 1

EP - 13

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1-3

ER -