TY - JOUR

T1 - Planar graph coloring with an uncooperative partner

AU - Kierstead, Henry

AU - Trotter, W. T.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1994/10

Y1 - 1994/10

N2 - We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: ℕ → ℕ so that for each n ∈ ℕ, if a graph does not contain a homeomorph of Kn, then its game chromatic number is at most f(n). In particular, the game chromatic number of a graph is bounded in terms of its genus. Our proof is motivated by the concept of p‐arrangeability, which was first introduced by Guantao and Schelp in a Ramsey theoretic setting.

AB - We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: ℕ → ℕ so that for each n ∈ ℕ, if a graph does not contain a homeomorph of Kn, then its game chromatic number is at most f(n). In particular, the game chromatic number of a graph is bounded in terms of its genus. Our proof is motivated by the concept of p‐arrangeability, which was first introduced by Guantao and Schelp in a Ramsey theoretic setting.

UR - http://www.scopus.com/inward/record.url?scp=84987487282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987487282&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190180605

DO - 10.1002/jgt.3190180605

M3 - Article

AN - SCOPUS:84987487282

VL - 18

SP - 569

EP - 584

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 6

ER -