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.
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U2 - 10.1002/jgt.3190180605
DO - 10.1002/jgt.3190180605
M3 - Article
AN - SCOPUS:84987487282
SN - 0364-9024
VL - 18
SP - 569
EP - 584
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 6
ER -